Why some pens stop to work when they still have ink?
Thanks for your attention.
Well, it can’t be all play and no work, so sometimes when a pen is doing too much playing, it must stop to work. Other times, the ink in the tip dries out.
The usual mechanism in cheap ball-point pens is the ball seizing up. You can sometimes free it by gently heating the tip with a flame.
It’s only been a month since the Stanley Cup series, and you’re ALREADY talking about such a sore subject? It’s obvious why the Pens stop to work…so everyone in Pittsburgh doesn’t cry.
Conventional wisdom (for 1970s era Australian schoolkids, at least) is that a period of rapidly rolling the recalcitrant Biro between the hands will warm things up enough to kick start ink flow.
From memory, it worked a lot - but not all - of the time.
Maybe the OP is holding the page vertically. Ball-points need gravity to function.
In case you’re interested, I see you’ve made a very common grammatical error for non-native speakers of English. I think it’s especially common among native speakers of Romance languages, because I don’t think those languages use infinitives and gerunds the same way English does. The grammatical way to ask your question in English is, “Why do pens stop working” not “Why do pens stop to work.”
This is not said in criticism. You speak English better than I speak whatever you speak at home. 
A ball-point pen can fail if the stops flowing to the ball. This can happen if the ink becomes too viscous (due to low temperature or evaporation).
If you drop a pen on its point the socket can go out of round. This can cause the ball to stick or the pen to leak (if the socket is damaged badly enough to create a gap).
I dunno, but I’ve found that if the heating trick doesn’t work, try bending the plastic tube containing the ink in half. Now squeeze. This forces ink toward the tip and facilitates flow to the ball point.
'Course, if the tube is the metal kind, you’re out of luck.
Not if it’s a space pen.
A pen might stop working even if the barrel still shows ink supply if:
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The nib/point/nozzle/tip/ball/whatever is clogged either with random junk, paper debris, or dried ink
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There are air bubbles in the ink chamber/cartridge/barrel
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The pen has been exposed to extreme temperatures
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The pen is being held at the wrong angle, or you’re trying to use the pen horizontally instead of vertically, unless it’s designed to work that way (space pen).
There are probably other reasons, including broken parts in the pen, et cetera, depending on the type of pen (ballpoint, fountain, gel, whatever).
Hope that’s a help.