If you'll notice what TC and Blagard said... you need to get to the climb speed you've decided on. If it's 160 mph in a bomber then;
take off
clears obstructions
go level (x key)
make sure you have all your flaps and gear up
type in /.speed 160 and hit enter
when your plane gets to 160 hit auto climb (alt-x keys)
The plane will begin it's climb at that speed. The Rate of Climb (ROC) will be determined by the speed you set.
Ok, now you've tried all of that and you are still having problems? It raises the concern that you may be flying with a mouse or have a stick that has not been properly calibrated. If you set climb speed and are using a mouse it might not be able to hold center close enough to allow auto climb to stay engaged. There's not much you can do about that. Alternatively, if your stick is not calibrated the same thing will happen as it will allow center point drift to the point the auto pilot will disengage. That's an easy fix. Just go
esc/options/controls/calibrate stick and follow the simple directions.
Everyone has personal prefs when it comes to climbing out. I'll share mine.
1) If I'm climbing out with a group in fighters. I normally take 10 mph off normal cruise climb so everyone can catch up.
2) When we are all together I normally set speed to 200 and advise I'm going to "WEP" to maintain a better ROC and burn off some off the drop tank (DT) fuel.
3) Upon reaching our acceptable altitude I call everyone the level altitude and we all go on auto level (X key). The term acceptable altitude is determined by your comfort level for entering the engagement area. For some, it might be 6,000 ft (6k). For others, 25k. You decide but if you're with a group go with the guy who might not like 6k but will settle for some middle of the road altitude of say 12k.
4) I try to get us up and level for a minimum of at least 5 minutes prior to entering the engagement area.
The reason for this is simple. You transition from climb at one speed and enter to a stable cruise speed for the given plane you're in. It takes time to get to that cruise speed. For example, a spit V might climb comfortably at 200 mph up to 12000 ft. But it cruises at 290 mph. From that cruise speed you have many options. You can dip the nose and easily get to 350 mph in a few seconds or just go straight up from level flight into an immelman or anything in between. Your engagement options are endless and you are less suseptable from BnZ'rs in the area.
When I climb alone I normally take off using auto take off then I use auto angle (shift-x) a lot and establish a particular ROC (like 2000 feet per min). I may adjust it as I climb to meet my own predetermined cruise alt to give me time to establish a good cruise speed. This gives me good forward, over the ground speed, while also climbing at a adjustable ROC. It requires a little more attention but I arrive over the contested area when I want, at the speed and alt I want fairly quickly and I'm ready to hang my shingle an accept all comers. It's a personal pref that I've been using for years and if you do it with others around you have a tendency to walk away for them when they're not looking.
If you need to go grab a drink or use the head...just use auto climb
Hope this helps.