First question, I was told LS trannys have single synchros while b16,gsr, itr have dual?

Situation: I had a b18b with Ls tranny which was good with no problems for about 6 months 6800 red line. Then I got a b20vtec 8500 red line and my 3rd gear started to grind at high rpms then it would pop out of gear until eventually it wouldnt even go in.

Got another used LS tranny was good for 1 month now 3rd grinds and 5th pops out.

Never mishifted either, ect. Just normal driving and everyonce in awhile high rpms.
Also have b&m short shifter.

I just want a good solid tranny that I can go to the track with and not worry about 3rd gear blowing up after a few track sessions. Is the Ls just not made for it?

Should I rebuild LS, or get b16, gsr, or itr? also explain why...