I found the replace-and-reinstall method was partially successful when using Infograph Modular in conjunction with another round timer-supporting face, but eventually the Infograph timer stopped updating.
But I can't get this to work at all with two Infograph faces; whichever face last had the complication installed gets the working timer while the other freezes. In fact if I replace the working complication with something else, the previously non-working complication starts working.
I've just been playing around with various faces and I've reached the conclusion that the reason I seemed to be seeing this more with Infograph is because those are the faces I use the most. I just tried it with two California faces and the same problem was repeatable there too.
Update: this might be key though. I just tried putting a non-Timer-complication California face between the two Timer-complication Infograph faces and now both of the Infograph complications are updating. There's a slight delay as the timers update from whatever digits they were on previously, but I think that's to be expected.
In a further experiment I then added the Timer complication to the California face and it froze while the other two either side of it carried on working.
At this point I thought I'd figured it out, and that the "rule" was that every other non-adjacent face would work while the ones in the middle didn't. So I added the Timer complication to a second California face at the end of the row for a total of four faces and... now only the first and last faces are working. The two in the middle are frozen!
Wow, this is bizarrely obscure. No bug bugs like an Apple bug bugs.
For now it looks as though the workaround for me is that, if I want the Timer on both of my Infograph faces to operate, I have to have another face (or faces) in the middle. If they're adjacent, or not at the ends of the selection of faces, one or other stops working.
Due to the way Apple provides zero feedback on non-developer bug reports, its unclear whether anyone will have read mine or followed the link to this thread if they did. If nothing happens in the next update I'll submit another report with these more specific details. It's all we can do.