Depends on the research, but I know you do lose combat upgrades. The research is automatically reapplied after you build enough replacement labs.

im not so sure actually,

just 2 games ago  i was in a fierce 1v1 battle with both of us having just our homeworld left,

i only had 2 militry labs  left,   so all i could build were LRF's and flaks,     i had 20 hoshiko's with the demolition-bots upgrade enabled, so i asked myself the same think you ask here,   so i checked my hoshiko's   and the demolition-bots ability was still active

also tried this in my singleplayer game after that on a few other TEC techs

strangely.. i never tried the colonize ability..

1. ships become unbuidable if you have unsufficient labs

2. ability upgrade for ships are not lost,   for example upgrading demolition-bots for your hoshiko's  even if you have 0 weapon labs  the ability remains (note that you cannot build the hoshiko's if you dont have enough labs for them....)

an excpetion to this is the starbase,   anything it upgrades stays,  upgrade it with a trade-port, and then lose all military labs,  the trade-station stays, but cannot be build on other starbases (not enough military labs error), or be upgraded to level 2

3. armor - shield - weapon upgrades  are NOT lost when weapon labs are destroyed,

4. resource upgrades stay, even if your tech level drops below the required, the same counts for planet capacity increases, Culture-spreading upgrades...  in fact everything that IMPROVES things (or previous upgrades)

note again that you cannot build trade ports, broadcast centers if your techlevel drops below the required level

so all this together 2 conclude,

any technology that improves already existing equipment only requires it to be researched,  you do not need to keep all the labs for the effect to stay  (shields,weapon, ship abilitys, resource increase etc.etc.)

any technology that would add something new to be BUILD requires labs, meaning ship-designs  starbase upgrades. if you have the technology researched  but do not have enough labs, you wil be unable to build it

again i note  that i did not try colonization yet,  i would guess  that the ability is removed if you do not have enough labs, but i have yet to try this

S_o_L

Yep...sometimes people who are in a serious pinch research the colonization techs, then scrap the civic labs to get a needed weapons lab built.

As a general rule of thumb, losing labs prevents you from building things when you drop below the lab number requirement, but all abilities and tech levels already researched stay functional.  I recall people saying that Super Cannons stop firing if you drop below 8 labs, but I have never personally been in this position nor gotten around to testing it for myself.

The super weapons do stop firing in my experience if you drop below tier 8. At least thats the case with the novalith in vanilla.

Actually, it doesn't fit the theory because other abilities are not lost.  That is why I mentioned it, it is the exception, right?  Trying to think of other abilities that could follow this other than superweapon?  I'm probably not a good person to know....people don't get my labs that often.