If you're having trouble with escapes, you should consider focusing on them in isolation. I don't mean putting in a ton of static repetitions, though that can be useful if you're really making a point of paying attention to the details and improving with each rep. Most people find that too boring to get too much out of it. I think you'll get better results if don't overdo static drilling and instead work on isolated positional sparring from wherever you're having trouble.
For example, start under side control and try to escape (return to guard, go to knees and takedown or reverse/roll them) while they try to pin and submit you and improve position. Reset and restart if either achieves their goal.
You can ease the learning curve by using progressive resistance, i.e. starting at 10% resistance and working up to 100% gradually as you succeed at lower percentages. Starting at full blast might be great fun for the top guy, but that's not what is going to help you learn and improve your escapes very well.
You can also refine the purpose of this drilling. You can also take this approach and apply it to really specific problems. If you're having trouble with escaping side control, figure out a specific problem you are having. Look at your posture, the placement of your head, hands, elbows, hips, knees, feet, etc. Where are they ending up? Where should they be? How can you get them there? Once you've worked this out and developed a solution, do isolated sparring for just that single point. Maybe even forget the rest of the escape for the time being and just work on that single issue.
As an example, you might find that you're ending up with your near hand out of posture. Analyse the situation and figure out some ways of getting it back where it should be. To drill this, you start out of posture under side control, with the goal of regaining proper posture; your partner tries to keep you out of posture. Reset and restart once you've achieved your goal or if the positions change enough to take you outside the scope of the drill.
It also helps to have a willing and helpful training partner. If he keeps getting you with something, he should be happy to explain how he's doing it. He doesn't need to feed you all the answers, but the learning stops if he just keeps trying to "beat" you without then telling you what he's doing and give suggestions on how to counter it. There should be a sense of cooperation and development.
I think training like this can be very beneficial, though most people don't put in the time and effort to do it. I know I could sure do a lot more of it.