I must be in a minority because it doesn't bother me at all not finishing a game.
Admittedly it doesn't happen very often that we don't finish a game.
Two occasions spring to mind one of a game never being played and one that would not end.
The first I think I've mentioned before As both of Us had just spent a week building a display. We thought a game would be a nice way to start the weekend. We set up the table both of us spent sometime looking at how pretty it looked. Then looked at each other and in perfect sync said"Pub?"
The unending game was a ten player game of Epic when we worked for GW( it was a compulsory game only way out .was to be wiped out.)It was a Friday afternoon So we played in suicidal mode. Tony was out in under an hour. I was planning Imperial Guards. I managed to destroy my entire force at a similar speed.With .... the exception of four stands of Rough Riders These little sod's would not die. They just kept sitting on that bloody hill and rolling six after six after six( I must have rolled just about every six I'm allowed in my entire life.because ever since they've become rarer than hen's teeth.) The worst part was this became a focal point for everyone playing .So I couldn't even claim to be wiped out.
The command stand lasted until 8pm passing modifier after modifier !and it was 9pm before we got out as everyone wanted to recount how they'd held out. Two hours after a couple of selfrespecting single Hull Lad's in their twenties would normally be in a pub on a Friday night.
Following Monday I sold the treacherous little buggers and have never played Epic again.
We tend to have set games in turns of hours rather than a set number of turns.