I find it very hard to complete an STF without getting dropped in the beginning, middle, or near the end. It has to do with craptics fail auto-removal system, which is apparently designed to kick players who leave the team. Please remove this system and just disable the leave team button in STF's, so players who have the same problem as I do can actually go through an STF without getting dropped in the middle.
I don't know if it's the same as the OP, but I have been kicked from Starbase 24 twice today. I don't know if it was a bugged system or just full, but it was kinda annoying to wait for the map to load and get You have been kicked from Starbase 24 and You will be kicked from the map in 10 seconds at the start.
don't think this addresses the OP's concerns...but re: getting kicked 10 seconds in:
don't queue from space, when around a planet or space station like ESD or DS9. Awhile back a patch that dropped in some new 'warp out' animations bugged the crap out of queueing from those areas. You warp in...the computer registers something funny...and it warps you back out.
Once we discovered that problem/quick fix we've queued from either the ground or from sector space. Haven't had a problem since. Hope that helps.