A greyed-out rival is paused because your plan has fewer rival slots than you have rivals. This usually happens when a paid plan ends.
Paused rivals are never deleted. Their history stays, and they come back as soon as there is room:
When a plan ends, the rivals you added yourself are kept active first, then the ones we suggested. The same goes for games: if you have more games than your plan includes, the extra games pause too.
Tip: your Overview tells you how many rivals are paused, so you never lose track of them.