Wikipedia's page about monarchies states that they might have "predetermined limits on the length of their tenure". However reading the page there is no mention about any current monarchy who does that.
So, do any current monarchy have such a system, either a simple "time limit" or something more complex? Voluntary abdication doesn't count, obviously.
If not, are there any (recent or ancient) notable examples of monarchies with such a rule?
The only modern day examples of monarchies with limited tenure are Malaysia and the United Arab Emirates.
"There are two elective monarchies, Malaysia and the United Arab Emirates, where the constituent states of each federation are hereditary monarchies but those rulers form an electoral college which assigns the federal position of head of state to one of their number for a term (of five years)."
source: Wiki page on Hereditary Titles
There are some other examples in there as well of some more ancient monarchies.
I'll look at non hereditary absolute rulers first, which are similar to monarchies. If you look up Dictator, you'll find examples of absolute rulers who had set terms. Roman Dicatators being the original example as well as Giuseppe Garibaldi.
Many states have or have had emergency power laws that effectively result in a dictator for the duration of an emergency (although sometimes this doesn't go so well, Article 48)
Protectors spring to mind as well. So do puppet rulers, colonial governors, Proconsuls and others who ruled like kings but bowed a knee to an external authority.
As for monarchies, recently with Queen Beatrice's abdication we've been reminded of Dutch tradition, where an aged monarch is expected to abdicate. But did you know it was also expected in Medieval Japan, where it was practice for emperors to step aside so the heir could ascend relatively young. In addition, before Meiji Restoration it was common for empresses (women) to rule for the minimum time until a male descendant was old enough to rule. Women leaders acting as a temporary "stop-gap". None of these aren't hard and fast term limits, but they are clearly informal limits on length of rule.
Roman king (rex) had a limited term of 8 years, but this was never observed. The kings manipulated the law to extend their term.
Under Diocletian the Dominate system was established in Roman Empire where an emperor's term was limited to 10 years. But only a few emperors followed this limitation, which soon became obsolete. But it is not certain whether Dominate should be considered a monarchy.
Consider Sparta.
In Sparta the king's (archagestes') term was 8 years. Upon its end, the ephores conducted a fortune-telling rite so to determine whether the gods were in favor of the term extension.
