yup - a flaky connection, but I would totally suspect the mechanics before the electronics:
Before opening it up:
1) remove the space, and dig around the whole area it wants to be with a smaller paintbrush, I use 1", normally for keyboard 'dusting'. This should sort out and/or allow you to detect any problem with the bar's actual movement.
2) look down the two shafts the keyboard rides in - one will have a spring and hammer at the bottom, the other will likely just have a nylon spacer to help the spacebar stay aligned. If you see anything in there, shake it out. If you have compressed or canned air, give it a moderate pressure couple of spurts to hopefully dislodge any cruft getting in the way of the hammer at the bottom. temporarily replace the spacebar with an ordinary key, this way to can check to see whether you successfully cleared out the problem, try again, etc.. a flashlight might help, and *gentle* poking at the spring to activate the hammer will both be fun and enlightening. Be careful you don't bend or pull out the spring, mind as fixing it is a black art.
AT this point yer keyboard is likely working. If not, in order to open and clean the membranes fully, a bolt-mod is likely needed. If you love your particular keyboard, then go for it - else consider switching out the tray with one from a used Model M of some sort... OK - someone else will need to tell you _which_ 90s Model M is compatible with the customizer, as I have neither a customizer nor any of the Lexmark 101/105s that the customizer is based on.
Alternatively, as pointed out above, getting a quote from Unicomp to service the board would totally be in order at this point. If you are still under warranty, you may not want to even bother opening it up with a 5.5mm or 7/32 long, thin socket.
(Oh, and to confirm the customizer has neither a nipple nor a trackball/pad, correct? - if it does, then replacing with an old board is not going to work. Finally, the old boards are almost all PS2, so to keep USB you are looking at service from unicomp)