I find backgammon fun to play more-or-less at every moment. Likewise the Reiner Knizia game Battle Line.
Off the top of my head I can't think of a game that I play regularly that I find to be not enjoyable in meaningful periods - maybe ship vs hip combat in Classic Traveller can have that problem? But that's probably why my Classic Traveller game doesn't feature ship vs ship combat, since I worked out that it's not really fun to play!
Well, as I've often posted, I'll put the verisimilitude of the settings in my RPGing up against what others seem to be doing any day of the week. And also the degree of "characters struggling in a fantasy world", as far as
my Torchbearer game is concerned.
The idea that the only way to achieve a verisimilitudinous game of character struggle is by making the game boring for the participants seems wrong-headed to me.