How long do you give them?

That's way too complicated for me! A lot depends on how much I want to grow the seed in question - is it rare, the only one I have, in which case I might be more patient. Some seeds are notoriously slow to germinate so I'll set the pots aside and forget about them.
If its something common, like today's old carrots and leeks, which were a couple of years past their sow by dates, I just scatter them and forget them.
I find "forgetting" seeds is very easy. I wouldn't waste time, effort and compost on old, common seeds.
I'm guessing that you have some particular seeds in mind?  Care to share?

Not really anything particular. Currently it’s many different varieties of eryngium that have not shown any signs of life. But with my seed hoarding, and not actually sowing very much the last couple of years. I seem to have a lot of past their best seeds. I will be using your scatter and forget with a few.