I have a new 2014 TI with Tramps and have sailed it over 12 times, many hours, and have not experienced your issue. I assume you are using Hobie brand TI tramps and not a knockoff. If so, it sounds like you probably have the tramps installed incorrectly. The front of each tramp slides over the front AKA with the cutout on the inboard side (closest to the boat). The pocket on the tramp should be on the top side of the tramp (there is a left tramp and a right tramp, this is how you can tell). The rear of the tramp attaches to the rear CROSSBAR and AKA with straps/clips.
When fully rigged, the inboard side of the tramp (closest to the boat) is secured to the CROSSBARS (front and rear) while the rest is secured to the AKA. The cutout on the front of the tramp should slide over the AKA hinge so the tramp is actually on the CROSSBAR with the AKA hinge visible through the cutout. You may have to rotate the tramp while sliding it over the AKA hinge to get it to fit. Once over the hinge, it fits perfectly.
Once the front of the tramp is positioned properly, I like to start with the center, rear strap then connect the rest. The inboard (closest to the boat) rear strap is strapped around the CROSSBAR on the inboard side of the AKA hinge. All other straps are on the AKA itself. Then tighten all straps as tight as possible, one at a time, then go through them again until you can't tighten them any more.
The last step is to stretch that little bungee loop on the front around the pin that holds the AMA bungee.
This setup will keep your tramps secure and should actually keep the AKAS attached to the CROSSBARS.
When I am ready to fold in the AMA/AKAs, I unclip the tramp, roll it up (secured using the bungees attached to the bottom), and slide the front cutout off the CROSSBAR, outboard, so the tramp is only rolled around the AKA. Once this is done, you can fold the AMA/AKA's and secure them to the hull. I have never had to remove the tramps from the front AKA since I installed them.
The AKA clips in the crossbars have worked fine and only come undone when I squeeze the buttons. I could see the potential for the AKAs pop out, however, if you apply enough force. You may have potentially damaged the clips when putting a load on an improperly attached tramp. You can check this easily by putting the AKA in the crossbar and pulling on it to ensure it is secure. Is should not pop out easily. (As an aside, I even have one AKA clip in the crossbar that is damaged. It only holds the AKA in with half of the clip but I've still never had it pull out. I need to figure out how to replace that clip. It's not as easy as you'd think.)
There is a good image of a grey tramp installed correctly: http://binksmarine.com.au/store/hobie/k ... ure-island
Let me know if this makes sense!