Boy, I had an Opus X Petite Lancero I started and about a quarter in got interrupted and couldn't finish. So I snipped all the way through until I didn't see anything but unburned tobacco. Put it back in my travel humidor. NEVER again. It took a month to air that thing out and get the stale as smell out. I tried the cigar a bit later once I got back and it certainly tasted stale. So if I may get interrupted for an extended time, I just smoke something I don't mind losing out on half.
Now relights really aren't an issue to me, especially if they are after a relatively short period of time. I have had to leave a cigar for an hour or two or even a bit more, knocked all the burned ash out and fired her up with very little ill effect. The only problem I have found is that weather conditions can be a detriment. Nasty, rainy, humid day and let it sit even protected and it will soak some up and affect it. Same for a hot day drying one out quickly.
But hey, if you haven't had a bad experience and it gets more value out of a cigar for you, good on you. Like was mentioned before, my only concern cutting a larger cigar in half would be the foot end unraveling without being constructed to smoke. That being said, I think I remember CI selling a huge cigar that was designed to be cut in the middle, I think they capped both ends, and you cut dead in the middle. So the thought certainly isn't new.