Breaker does not make solid connection even after replacing it
My panel is a 48-year-old GE Flush Type TX1615F Mod 2.  I have never had a problem with loose contact of breakers. Is it possible that you are not pressing it in all the way? 

I have installed a THQL1120GF and a similar 15A, but all my other branch circuits are protected by the thinner (1/2 inch wide) breakers which I think are THQP. If your panel allows these breakers, then try one of these. Two of these would fit in the space of one THQL, right? Their clamp is at a right angle to the clamp for the THQL. If you install only one, put a 1/2 inch spacer next to it.

EDIT
My GE panel accepts both THQP and THQL breakers. The panel and the breakers have a mechanical interface to prevent improper insertion of breakers--these prevent the breaker from snapping in if it's not allowed there. I came up against this when I tried to put a 2-pole compact breaker in a single 1-inch slot instead of astride two slots. A THQL must go into a single slot and presumably also has protection from improper insertion astride two slots. Are you putting these THQLs in a single slot?