I've got the Timney skeleton trigger also, and I had the same problem. After firing a round, the trigger would not reset, but I noticed that if I rotated the fire/safe selector to safe and back to fire it would fire once more. After a frustrating hour at the range, it stopped resetting even with cycling the safety selector.
When I got home, I called Timney and talked to a fella named Jason. He asked if I was mechanically inclined and willing to try letting him talk me through a fix, otherwise he was willing to repair/adjust it in-house but I'd have to ship it to them.
I tried it myself, and all it really needed was a 1/4 to 1/2 clockwise turn on a tiny set screw that is in the centerline toward the rear of the unit. It had a little blob of orange hard plastic anti-tamper stuff on the screw head, but once past that, I made the adjustment and it runs beautifully now. I assume, of course, that your 2 set screws that set tension between the trigger housing fixture and the floor of the lower receiver are already tight.
I'm a little concerned that the missing anti-tamper material on the screw head would void my warranty down the road and nobody would believe or remember that Timney's own people suggested the self repair, but it is a lifetime warranty and I felt comfortable after talking with them that they are proud of their product and had a good customer service attitude about honoring the warranty. The anti-tamper blob looks like it could be dislodged from normal use and cleaning anyway.