I have replaced many a second gear, that is what they do when the engaging dogs and mating slot in the gear round off. You have to split the cases and replace 3 gears and one shift fork to repair it right. 2nd, 3rd and 4th on the driven shaft. With almost 30K on the bike, you should replace all main and rod bearings, in other words, you are looking at a major overhaul. If you can't do the work yourself, you may want to sell it and get a newer one.
Good job BHolland on the info, sounds like you have been there before!
another note after 30K,,,the shift drum too.....another $80.00 (Dealer)
on my dragbike it cost about $575.00 every time (from the Dealer) I have to fix the second gear problem. And you don't have to split the cases but you will have to pull out the motor ( best to fix the trans on bench with motor upside down). and yes if you are going in that far you might as well freshen up the motor.
But I launch @ 6600rpm and shift @ 10,000 Air shifter (no clutch lever)
w/ engine kill.
The second gear jump out prob will only get worst and not better over time! The good news is Suzuki trans come back cut for the factory and this problem does not happen very often, unless you miss some gears over time or give it hell like I do!
Brent