The problem isn't "we can't come up with a definition of life", it's "every time we define life, we don't like the results".

We could make up any definition. The problem is that we instantly think "well, that's stupid, let's define it again". But I'll say it again, that wasn't ever the problem. The problem was when we thought we were talking about one thing, but we were really talking about something else - our own personal heuristic.

And nature doesn't care about your heuristic. Hueristics make terrible definitions.

Virus's are alive by a lot of heuristics. They act alive-ish. They're not alive by a lot of definitions. Bacteria are one species by definition. But since that's not useful, we make up heuristics that separate them into all sorts of species. Go through every situation, every time we are disappointed with the definition of life, and we find that the reason is that we just don't like it. We WANT something else to be called life, because it feels that way.