As far as I know the only effect of losing research stations is that you cannot build structures and ships that are dependent on the research. I don't think you can fire Level 8 superweapons either (the sailors manning the super weapons just "forget" where the big red fire buttons are located at), though this is really only an issue for the TEC since it doesn't make sense to build the "super" weapons for the other two races.
For example, if you are Advent and you have a total of 3 Weapons Labs up and you've already researched Illuminators, if you scuttle one of the weapons labs (or if one gets destroyed) leaving you with 2 weapons labs then you can no longer build Illuminators until you have 3 weapons labs again.