Ice ages combined with a Mediterranean type basin
Your planet has the following features:
a more extreme climate than Earth, perhaps because it has very high obliquity or perhaps because it is an eyeball planet. Because of this it has very large ice sheets at the poles (or dark side) and a region at the equator (or sunlit side) that's so hot that ocean water readily evaporates, leaving salty desert or a body of salty water like the Dead Sea only much bigger. It might have less water than Earth, to facilitate these features.
a strong seasonal cycle that lasts several thousand years. (I'm unsure of the orbital mechanics needed to achieve that; it could be worth an extra question if there isn't one already.)
a particular quirk of topography, described below.
Your civilisation lives in and around a basin in the temperate zone, somewhat similar to the Mediterranean basin on Earth. The basin has an opening where the water can flow out into the hot region. But this opening is far to the North (or South or towards the dark side, wherever it's cold), so the water has to flow North and then turn around and flow South again, until it eventually reaches the hot region. The basin floor slopes downward slightly towards the North, and the opening is deep enough that the entire basin can drain out through it.
But because of the seasonal cycles, this opening is blocked with ice most of the time. As the planet slowly starts to get warmer, the ice sheets start to melt, and this fills up the basin. (So this will be a freshwater ocean.) In the hottest years of the cycle, so much ice melts that the opening strait becomes unblocked, and at that point the entire basin suddenly drains. Once that has happened the water will flow to the hot region and start to evaporate. The evaporation explains why the water can flow downhill instead of just meeting another ocean. The evaporated water will ultimately fall as snow on the ice sheets, replenishing them.
After this, the basin will remain dry for most of the thousands-of-years cycle, until the planet has cooled and heated up again and the melting ice refills the basin.
If desirable, the cycle could be shorter, say around 100 years or so, but the ice doesn't usually melt enough to drain the basin. This means that the oceans will fill up much quicker, since the ice will be melting again only 100 years after the draining, but it also means the draining will be much less predictable. A hundred year cycle could be achieved by having your planet orbit a brighter star than our Sun, at a larger distance.