As always, the FIRST Wiki is full of useful information. I direct you to
Index of teams by age.
FIRSTwiki suggests that all of these teams are about tied for oldest, having survived since 1992:
- 20 (The Rocketeers)
- 45 (TechnoKats Robotics Team)
- 126 (Gael Force)
- 151 (Tough Techs)
- 190 (Gompei and the H.E.R.D)
- 191 (The X-Cats)