My French carrage clock stops at 7 minutes past every hour?

There is no maker's name on the clock; but it is brass framed, circa 1900 and 16 cm high. It has three winders - one for the gong, one for winding up and the other little one is for the hands. It works perfectly until it gets to 7 minutes past the hour when it stops. The minute hand seems to 'stick' at 7 minutes past, because when I move it with the key it is very, very stiff. I haven't taken the clock to bits - yet - as I would be nervous of a spring springing and being unable to get it back in to place. I did try wiggling the minute hand over the bit it sticks, to try and 'release' whatever is stopping it, but it didn't work. If anyone has any idea what to do, please let me know. Thank you.