I had the same problem with my little one! It was crazy! After they do it once, they do it over and over again....Gracie2006 had some great ideas. What I ended up doing was hanging towels or sheets over it...something thick so they can't climb up it...however, then you can't see them. A shower curtain sounds like a great idea.
If you don't mind going out and buying another gate, they do have gates that are slanted at the top so that they can't get out. Or you could get an actual crate where it's gated on all 4 sides. It's up to you.
You might try giving him a Kong or some special treat that he ONLY gets when he is in his pen. That's what I heard you are supposed to do when you are working on separation anxiety. So that way, he'll look forward to going into his play pen because then he gets his favorite treat! I used to fill a small Kong with peanut butter and freeze it...she would go crazy with it for hours!!
Another idea: you can sit there for the first couple times you put him in it, and have a water bottle at your reach. If you're on the couch or whatever, and see him trying to climb the sides, you can squirt him with the water. We do that for Lola's barking and it works wonders. Even if it makes you sad to do it, they DO need training, and WANT it. They forget you squirted them in 2 minutes and love you just the same! Those are just some suggestions....Good luck! I had the same problem!! Those little rascals!