Do Calendars repeat? If so, how often?

Yes, calendars do repeat. As there are seven days in a week which begin the year and month, you would expect that in every sevens years there would be a repeat in calendar. However, the leap year, which is once in 4 years complicates the calendar. The calendar can repeat at 5, 6, 11 or 28 years. The only confirmed pattern is that of 28 years. The 28 year cycle works well as long as the 4 year cycle of the leap year continues.

In Gregorian calendar, century years not divisible by 400 is not considered a leap year, for example 1900 and 2100. We are currently in 4 year cycle of leap year from 1904 - 2096 and 28 year cycle is maintained. For example, your 2010 calender can be used in 2038.