I've been through the rules 3 or 4 times now and I'm still a little foggy when it comes to understanding Engineering points.
My current, conservative interpretation is that any time you do something that grants EPs, you are compelled to spend them then and there or they disappear.
However, I can't find anything in the rules that spells that out explicitly. I was initially confused about whether or not you can carry around a stash of EPs to spend later. The main thing that makes me doubt that is the lack of any sort of token for tracking accrued EPs... if you were able to bank them, I'm guessing the game would provide a counter of some sort.