You can put a small drop of very light oil on the base of the shutter release itself, to get it to go inside the mount as you push the shutter. Very small, very light, then wipe off what you can after pushing the shutter a few times.
The other possibility is that there is oil around the base of the shutter and it is gumming up a bit. This will cause the pressed metal ring with levers on it to not return as smoothly as it should (the spring Hans mentions attaches to one of these levers and pulls the lever back towards the shutter release after use).
I had a T that had a super-loose shutter lock. After firing it seemed to rotate a bit toward the lock position just because... well, it just did. Check out the lock to see if it is loose and/or moving.
By the way, does winding the film push the shutter release back out? On some cameras like this, the cocking of the shutter during winding will also move the ring with levers. I don't remember the action of the T on this.
All in all, if this is the only issue I wouldn't open it up.