*.tile.openstreetmap.org is timed out

FWIW, the server from which your tiles are served seems to work for me:

Pinging baku.tile.openstreetmap.org [94.20.20.55] with 32 bytes of data:
Reply from 94.20.20.55: bytes=32 time=105ms TTL=54
Reply from 94.20.20.55: bytes=32 time=105ms TTL=54
Reply from 94.20.20.55: bytes=32 time=105ms TTL=54
Reply from 94.20.20.55: bytes=32 time=104ms TTL=54

What does a traceroute have to say?

Thanks for quick response, SomeoneElse. I think this is a political issue, since I request the tiles from Armenia, whereas tile.openstreetmap.org redirects to baku.tile.openstreetmap.org (to Azerbaijan). It seems, they blocked all requests from Armenian IPs... So, I guess it's totally against OpenStreetMap's policy!