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sometimes, on a multiplayer game the tech slots dont work and we are forced to rehost. the problem is that the play with that problem will lose one tech allredy made
Sounds like host and joining player's system got (slightly) out of sync. Ie. the client thinks research project has ended, but for the host it's still not at 100%.
Rehosting will use the host's view of the game. Which will explain why the tech is no longer present.
Multi player specific, so I'll move you over to the experts. Maybe they can come up with a better or more detailed explanation.