Are there any countries that impose term limits for mayors? Are there any good arguments in favour of such a rule? I could only find some links about the ambiguous situation in Portugal,
Yes, but not many.
Wikipedia has a nice chart for comparing term limits across countries, but I can't say how all-inclusive it is. I can say that it at least gives a reference for Taiwan, which sets term limits for mayors at two consecutive four-year terms. This is found in Articles 55/56/57 of the Local Government Act, with separate sections for special municipalities, county/city, and township/city governments:
The county/city governments shall have a magistrate/mayor, who shall represent the county/city in external affairs and administer affairs of the county/city. The magistrate shall likewise oversee the self-government of townships/cities under its jurisdiction. The magistrate/mayor shall be popularly elected to a term of four years and may be re-elected to a second term.
Wikipedia also lists The Phillipines as having terms limits of 3 three-year terms for "all other local government officials," which I assume includes mayors. Unfortunately I can't find that reference.
Arguments for/against mayoral term limits are largely the same as they are for other positions to me.