Update:
The tivo remote is not a learning remote, but it can be programmed to transmit a couple of commands from other remotes by inputting manufacturer codes on the keypad. So I programmed it to know the volume buttons for my denon receiver.
Then I tried a couple of variations:
(1) learn from denon, press-to-hold on denon
Result: repeating works
(2) learn from denon, press-to-hold on tivo
Result: repeating works!!
(3) learn denon code from tivo, press-to-hold on tivo
Result: repeating works!!
So I broke out the smartphone camera and looked at the IR transmitters and this is what I saw:
When the denon remote transmits it blinks fast enough that the IR light looks almost continuous
When the tivo remote tranmits a denon code it blinks at about the same rate as the denon
When the tivo remote transmits a tivo code it blinks much slower, slow enough to see the on/off transitions
I looked at the IR blink rates on two other remotes. Flirc does hold-and-repeat with both of them OK:
sony remote - IR light looks almost continuous
wdtv live remote - IR visibly blinks, but blinking is slightly faster than the tivo