Hi everyone.
My car won’t start.
Another:
The ink on my face won’t come off.
In both sentenses the present progressive tense is implied, but auxillary verb (will) is used.
Can you please, explain me, why is that?
Why can’t we say:
My car isn’t starting :).
The ink on my face isn’t coming off.
And what about positive sentenses using will, but implying the present progressive tense in sentenses? I can’t come up with one. Is it possible?
Sorry for bulky explanation.
As far as I can judge, we’re dealing with ‘something will not work/start/open etc’ expression which has nothing to do with implied present progressive tense.
The expression “used for saying that you cannot make something do what it should do, although you have tried.” (And here you’re implied to murmur something ‘encouraging’ under your breath: “Come on! …!”)
Good question! I could be wrong, but:
“won’t” is used here to talk about unwillingness or refusal to do something and it relates to present situations. This use of “won’t” also implies an ongoing situation.
Here is another way of saying the same thing, for your two examples:
My car won’t start. – My car refuses to start.
The ink on my face won’t come off. – The ink on my face refuses to come off.
This is just about all the explanation I can put together right now. Anyway, I’m sure the experts will reply soon! 
No need, you have!
I still stick to my guns: in my view, “unwillingness or refusal” as a possible explanation isn’t the best option here. “My car refuses to start.” sounds as if your car was an animate creature, like a horse refusing to obey. “The ink on my face refuses to come off.” sounds even more ambiguous.
The dictionaries I’ve consulted define ‘refuse’ as a verb referring to subjects rather that objects (you can check it).
The way I see it (and the Macmillan’s clearly indicates it): I’ve tried a few times to start my car/rub the ink off my face, but to no avail. Situation is still the same: the car doesn’t start, the ink is still here, on my face. And that’s not because of ill-natured car (which ‘refuses’ to start) or the ink (which ‘refuses’ to come off). Maybe I wasn’t diligent enough (or the ink turned out to be permanent,…) so I must do it again or use Plan B…
I can see why you think those might be wrong, but actually “My car refuses to start” and “The ink on my face refuses to come off” would be OK in informal English.
It’s personification and I think it would be acceptable, even in some more formal forms.