At the end of the battle the RAF was seriously depleted of experienced pilots, and those that were still alive were exhausted and showing all the signs of combat fatigue. Most of the RAF pilots were by then greenhorns with very limited training ... just like the Luftwaffe pilots at the end of the war.
I don't know of any complete study that looks at the number of pilots the RAF had at the start of the battle who were still there at the end, but Stephen Bungay gives the figures for 501 squadron as an example.
501 was the only squadron that fought in the south east from the first day to the last. They had higher casualties than any other Spitfire or Hurricane squadron, with 18 pilots killed during the battle. Of the 18 killed, 3 (or 4, Bungay's maths doesn't add up) were present at the start of the battle, 15 were replacements who arrived after the battle started.
Of the 18 men in the squadron at the beginning, 8 were still flying with the squadron at the end, 2 had been transferred to other squadrons and were still operational. 3 (or 4) had been killed, 5 wounded and invalided out.
As I said, 501 squadron had the highest losses of any of the squadrons at 18, the average for Spitfire and Hurricane squadrons was 8.4
The average squadron had less than half the losses of 501. If you assume they lost the same proportion of original/new pilots, then the average squadron of 18 pilots at the start of the battle lost 4 or 5 to death and serious injury, and kept 13 or 14 of the original pilots operational.
As to exhaustion and combat fatigue, this applies more to the Luftwaffe, that was flying longer missions across the Channel without rotating pilots. Ulrich Steinhilper gives some examples:
What we were seeing, although we didn't realise it at the time, was our first case of KanaIkrankheit (Channel Sickness). A combination of chronic stress and acute fatigue. At first there were isolated cases but, as the battle dragged on, there were to be more and more cases of the evil disease. The symptoms were many and various but usually surfaced as stomach cramps and vomiting, loss of appetite and consequently weight and acute irritability. Typically the patient's consumption of alcohol and cigarettes would increase and he would show more and more signs of exhaustion. There was little leave and, unlike the RAF pilots, wc were not to be circulated to quiet zones for short periods of rest and refitting. There was nothing our doctors could do either. The principal of battle fatigue had not yet been established and it was felt that as soon as anyone was taken out of the line because he was showing signs of stress, there would be a flood. So the doctors resorted to diagnosing appendicitis. This minor operation ensured that at least a pilot would not be flying for about two or three weeks.
Part and parcel of Kanalkrankheit were the symptoms which affected the aircraft. Instruments would fail, motors would run hot or lose oil pressure, just to be remedied by returning to base. Ground crews would spend time chasing a fault through a machine only to find nothing amiss. Following a Werkstattflug the aircraft would be pronounced fully mechanically fit for service. A few hours later it would be back with guns that would not fire in the air, but which let loose a hail of bullets on the ground. The groundcrews were faithful to their pilots, and to their credit tried to cover for them, but when there was no chance of finding a fault the former had to speak up.
We all felt the strain but when, in the middle of August, the command reshuffle took place, there was damned near a mutiny in our Cruppe. Our Commander, Hauptmann von Eschwege was called up to Luftflotte 2
Headquarters and returned with the Iron Cross First Class. It was arranged for the pilots of the three squadrons to be paraded at their separate dispersals whilst von Eschwege made a short speech in which he explained that it was with great regret on his part that he'd been relieved of command of I/JG 52 because of a grumbling appendix. He wished us all "Good Hunting" and many victories and left for his appendix operation and thereafter on to a relatively safe seat at the fighter training centre at Merseburg.
There was almost uproar amongst the pilots, not only because of his Iron Cross, but also because he was effectively being rested whilst we were still having to remain at the sharp end of things. This wasn't the last time that the strings would be pulled for some of the more senior officers and it is significant, I think, that during the Battle of Britain our Gruppe never lost any personnel of the rank of Squadron Leader or higher. Hauptmann Wolfgang Ewald replaced von Eschwege as Gruppe Kommandcur and inherited quite a disconsolate brood of fighter pilots.
In the context of fatigue it's worth repeating that line about 501 squadron again:
501 were the only squadron to remain in the south east from the start of the battle to the endUnlike the RAF the Luftwaffe did not replace their losses as quickly (almost not at all), so while the Luftwaffe did lose a third of their strength in the battle the remaining strength was not made up of greenhorns, but veterans. And the Luftwaffe was still a superior force in numbers.
Not in terms of fighter pilot numbers. The RAF by early September had about 900 - 1,000 Spitfire and Hurricane pilots fit for duty, the Luftwaffe just over 700.
"Contrary to general belief and official reports, the enemy's bombing attacks by day did extensive damage to five of our forward aerodromes and also to six of our seven sector stations. There was a critical period when the damage to sector stations and our ground organization was having a serious effect on the fighting efficiency of the squadrons, who could not be given the same good technical and administrative service as previously......... The absence of many essential telephone lines, the use of scratch equipment in emergency operation rooms, and the general dislocation of ground organization, was seriously felt for about a week in the handling of squadrons by day to meet the enemy's massed attacks, which were continued without the former occasional break of a day."
Report by Air Vice Marshal Keith Park - 6th September 1940.
To which I'll give you Dowding's reply:
I agree with the Air Officer Commanding 11 Group that the damage done by air attack to aerodromes has been serious, and that it was begining at one time to affect materially the efficiency of our fighter operations. Nevertheless, I must point out:
(i) That 13 aerodromes in the Group underwent a total of over forty attacks in three weeks, but Manston and Lympne were the only two that were unfit for day flying for more than a few hours
(ii) That although the scale of the attack certainly exceeded the capacity of the works orginisation existing at the outset, this was rapidly strengthened, and I do not wish to express any dissatisfaction with the measures taken to effect this improvement
The problem for the Luftwaffe is that in the last week of August they began an all out attack. They threw everything they had in to the battle. That wasn't something they could maintain indefinitely. Indeed whilst they managed 4700 fighter sorties in the last week of August, they only flew 4,000 in the first week of September.
I'd agree with you that if the Luftwaffe had maintained the same level of effort they managed in late August for several weeks, it would have had a serious effect on the RAF. But how can a force with declining strength and no reserves maintain the same, maximum, level of effort for weeks on end?
The Luftwaffe lost 111 109s in the last week of August. They lost another 129 in the first week of September. Continue that level of losses for another 3 weeks, and the Luftwaffe would have lost about 550 in a month, when production was running at about 150 a month and reserves were non existent. This wasn't something the Luftwaffe were capable of doing.
In the same period the RAF was losing about 135 fighters a week, so in a month about 600. But British fighter production was running at 470 a month, and the RAF on 6th September had 127 Spits and Hurris in storage ready for immediate issue, another 42 ready within 4 days, and 80 awaiting issue.