Perhaps I'll answer your question with another question - normally I wouldn't but in this case it makes sense to.
Provided you're not being tempted by this person, how long will you wait to make a decision?
If you do not feel tempted, and this person is not pushing you towards sin, then theoretically you could stay with them as long as you wanted. But it seems you already know it can't cross into the marriage threshold until they are saved. If not 2 Corinthians 6 has something to say about it. It doesn't say you cannot be friends with an unbeliever. You could theoretically date this person your entire life as long as sin wasn't involved, but I doubt you'll want to do that.
[SUP]14 [/SUP]Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
I strongly advise you do not issue an ultimatum to an unsaved boyfriend that he has to get saved or you're moving on, because that tends to create non genuine conversions. The answer is to continue being a witness for Christ and to patiently wait things out if that's the road you want to go down. But ultimately, if there isn't a genuine conversion, this is a road that must end if you ever wish to marry down the line.
So again, how much time are you willing to spend on this. As long as your unsaved boyfriend respects the tenets of our faith and isn't pushing you to break them, then you could stay where you are for quite some time, but ultimately I would bet you want to get married.
Whatever you do, do not compromise and marry an unbeliever. Not only is it specifically against God's Word, you'll be in for a lifetime of heartache. Every morning you wake up next to this person, you'll know they aren't going where you're going. And if you have children, it's confusing to them which religion (or lack of religion) they will follow (and here's a hint, they pick the easier path 9 times out of 10).