Al1943 mentioned a common problem of these triple shifters accessing the 3rd ring click position with the derailer limit screw forcing the cable to stretch forcefully. The shifter then refuses to downshift untill the cable tension is relaxed either by un-bolting the cable stop or momentarily pushing the big lever further stretching the cable then immediately applying the downshift, which actually works well in the field.

The best preventive for these over-shift problems is to keep the cable tension (and hi-limit screw) snug, so that it thus becomes all the more difficult (harder) to access the locked-out 3rd click. Note that deteriorated cable or housing can also make the 3rd click a little too easy to access.
Adjustment with these shifters used on doubles should allow virtually no "overshift" when accessing the big ring, i.e. the derailer should not momentarily move past it's high-gear position and then spring back away from the hi-limit screw when shifting up to the big ring.

As far as the O.P.'s problem, the little lever's pawl seems not to be engaging, a common problem on older shifters in cold weather but not newer ones. Something's either broken or the cable spool's ratchet wheel has some junk or strand of cable filling up one of the notches, acting like a ramp and allowing the pawl to slip past. Perhaps the pawl or pawl spring has broken, it's not unheard-of. Again, frayed cables in the shifter can cause a variety of ailments.