the synchros are worn, and when the teeth on the rings wear down it will some time cause grinding or in your case poping out of gear. looks like you will need a rebuild kit. i have rebuilt my t45 twice since I have had my car in one year. they are junk! see if you can get a tko, or t56, although you will want new gears if you go with the 6 speed because I have heard that first gear is very tall, so tall that some can hit 60 mph before they need 2nd. you will be looking at a new driveshaft and crossmember if you do swap out the t45. you will pay soo much labor to fix the t45 that it pays to just get a new, better one. d&d performance seems to be the popular choice here.
My t45 does the exact same thing, but in second gear. I was told that it might be a bent shift fork. I dunno, taking it to get an estimate next friday the 10th. If it's more than $500, then I'm going w/ a t56 and waiting another year for my vortech. Is there anything else, besides the driveshaft and crossmember and fluids of course, that I'll need? Will the computer need to be reflashed or anything, or is it just a bolt on sorta thing?
ya, your problem seems all too familiar and if you can in any way, Id go with another tranny all together. I hear they just bolt right in with some minor mods (about $3k total), and I have heard nothing about a reflash. But someone posted that they had trouble with their viperspec t56. I would want to make sure I got the exact one that went into the 03/04 cobra's right from the factory. But, that tall first gear will be an issue without an aluminum flywheel and supercharger to help get you through it haha. Check on one of those new tko's that just came out beginning of 04. They will take the expspensive synthetic fluid instead of that mercron stuff were used to though. but good luck and Id like to hear how you make out.