Microsoft Mobile RM-944 (Nokia 108) won't recgongnize specific SIM card.

That SIM card (it's SIM card from Serbian Telecom), works great with other phones i tried (Samsung S5230 Star II, Nokia 6310, Nokia 1100i, Nokia 220). Is the problem by the SIM card or something else. Other Telecom's card works fine in that phone.

What's the problem?

If the same card can work in other mobiles but not yours, either the contacts are dirty or the phone has become faulty. Try to clean the contacts if you can or get your phone checked

But also check with another SIM card, preferably from a different carrier