Pulled apart a transmission that was giving me trouble in the race car. I was having trouble upshifting into 4th gear - sometimes but not always it would not go into 4th - no grinding, the lever just wouldn't move into 4th. A couple more tries and it would go in.
I disassembled the trans and I really don't see anything obviously wrong other than 2 possible items that I don't think match the symptom:
1. the clutch hub key spring on 3rd gear was installed backwards and has become deformed so only holding up one of the 3 keys.
2. One of the "lockout" cylindrical ball bearing things that sit between the shift rods MAY have been missing - it's missing now, and I haven't found it in the work area anywhere.
So, dumb question - I have heard people say the shift forks can get bent on these - is that something that would be visible or measurable? The fork is a cast part that is very rigid and seems more likely to break than bend.
What else should I be looking for?
Might help if we knew the brand and model.
Assuming we're talking 1st gen Rx7 here. The only time I've had issues have been due to me and generally the issue I have is I end up in 2nd not 4th. Found how I place my hand on the shift knob to be critical. If my thumb is on the top of the knob with fingers on the far side it'll go into 2nd, if the palm of my hand is on top of the knob with the fingers down front it goes easily into 4th. Weird to have to train myself this on the track since I've always driven a manual.
So I suspect this doesn't help you.
Do the shift rods have some oil on them or are they dry? Mazda requires some oil in the shifter body.
Are the shifter bushings worn?
ha, guess so. 
FB RX7, which is extremely similar to a Miata transmission.
But kind of just looking for general causes of manual trans not dropping into a gear. Initial inspection didn't reveal any obvious problems. Thought bent shift fork might be more subtle, the ones I have "look" fine and also don't look very bendable.
This trans was built by a race shop several years ago and has probably 40 or so sprint races on it. Working fine other than sometimes pretending 4th gear doesn't exist.
Things I checked:
- no cracked synchro rings, broken springs, chipped teeth, bad bearings, etc.
- The little teeth in the clutch hub show some wear vs new, but I would expect they would cause more of a grinding problem than a no shift problem - maybe wrong about that.
- The shift finger clearance on the actuating rods are in spec.
- synchro fit against gear is in spec per service manual.
Also scratch item 2 from orig post as a possible issue - cylindrical ball bearing thingy back in custody after cunning escape attempt - trying to quietly blend in with the floor sweepings...
How about the shift turret? I have no idea what an fb RX7 transmission looks like but I had issues with the bushing in the shift turret keeping me from being able to get into certain gears occasionally in my RX-8. May not be applicable in this application but figured I'd throw it out there.
