Why did Tywin stop at 3?

As a show watcher only (so far), I'm intrigued if there is an actual reason given, either in the show, that I may have missed or the books as to why Tywin simply doesn't re-marry and keep on creating a larger bloodline with more children. As soon as Jamie joined the King's Guard he could have been doing this, right up until the events of the show. We see him struggling to rein in his 3 children and getting them to act on behalf of "the family" but this seems an obvious solution to me regardless of his age (ahem, Walder Frey). Was it superstition that he'd breed more Tyrions, who they see as a curse, or loyalty to his deceased wife (seems unlikely given his whole purpose is to strengthen the family legacy)?

Edit: Just to say thanks to all the replies (lots of them!). Some good insight and context given. Have to say I'm suprised that the popular answer was love for his wife. I wonder if the show should have done more to convey this as his character seems at odds with his actions sometimes. Don't get me wrong he's actually my favourite character and not everything should need spelling out I guess, after all the mystique of characters convictions is one of the biggest draws in GoT!