Well, no solution, just a comment: My mod has a lot of units added, and if you get all techs, you can quite easily have 80 units or something in the sidebar (all minus the side-specific ones) – yet I never encountered this problem before.
Therefore, I personally would take three possible causes into account:
1. Your memory. Like Arg hinted, perhaps your machine just runs out of it; might especially be the case when there are lots of animations and particles with translucency on the field.
2. You game. Did you patch to the latest version? Or perhaps you just fragged your game in another way...very unlikely, but still possible.
3. Your rules. It might sound very general, but if it's neither your machine nor your game, it can only be the tags you added to the original rules.
Although I pretty much doubt you could create something like that via simple code bugs. Memory is the most reasonable explanation atm. I suggest testing the mod on a different machine. (Don't you have any beta-testers you could bother with this?
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