How long can a lone rat stay a lone rat before it’s a health risk?

I know the general answer to this is not at all, but I’m referring to a rat I’m trying to find a home for and struggling to. He’s the last boy I’ve got and I’m in no position to get new rats at the moment.

I let him out when I wake up and he’s with me literally all day until I go to bed, so he spends 16-18 hours in my company every day. But he’s been alone for 2 weeks now and I’m worried he’s going to get terribly depressed. How long is it safe to keep looking for him a home before I have to get him cage mates?
As I said I’m not in a good place to get additional rats right now.