While switching on the AC in my Fabia the blower switches off every 5 to 10 mins ..I checked the fuse in fuse panel it was hot.

can anyone suggest what must be the reason ? 

I'd think that you could only check that the fuse and its connecting terminals are in good condition and that it tightly grips the fuse, any point like that in a circuit should normally only get warm/hot if there is some circuit resistance at that point and so volts are getting dropped > leading to getting warm/hot.

Perhaps when it overheats, the fuse becomes dislodged, breaks contact then cools down, re-makes contact and the cycle starts again.

 

This can happen on electrical with weak joints, soldering, etc. I this k the term is a "Dry joint". Worth a check. Have a gander at the fuse as soon as the blower stops and perhaps wiggle it a little or even fit a new fuse in, just in case the old one is a bit "Iffy".

If the fuse heats up badly it suggests a high current through a poor contact.

Clean / change the fuse blades and check whether the prongs grab the fuse properly.

If you can measure the current draw of the AC.

 

Your AC might switch off because something inside heats up and switches off as protection, but check the blower switch. It works with a big resistor to reduce current in lower settings for lower fan speeds. The contacts can corrode.