They won't count evolutions that are not done correctly. You can keep trying if you rest in the approved position(s) and there is time remaining. For example, if you're tired of doing pushups after one minute, you can rest in the "up position" until you're ready to go again -- assuming, of course, time remains in the event. Or you can just stop early (either b/c you've maxed out or b/c you can do no more). You don't have to try for the full two-minutes if you don't want to. It's a max time, not a required time.
If you continue to have trouble performing an evolution correctly, it may make more sense to stop and conserve your strength for the next event than to continue expending energy without any benefit. For example, if you fail to complete two pull-ups in a row, it's unlikely that you are suddenly going to get the burst of energy needed to do one correctly. Thus, rather than keep struggling to do another one -- and burning energy -- when you're not likely to do another, you probably should quit that evolution and move on to the next one.