Generally, in any polytheism, the gods all have roles: god/goddess of thunder, god/goddess of fertility, god/goddess of pain, etc.
Since they have roles outside of inhabiting a mortal, there are many reasons one would choose to leave.
I am a god of infinite power and cosmic energy. It is through my will alone that causes the sun to rise and the plants to grow... And we're having scrambled eggs for breakfast again. *sigh*
There will always be the "cool" deities; the ones that deal with war, power, death, life, growth, and so on. This means they get chosen all the time. After a while, they will get bored of being inside a mortal lifetime after lifetime. All mortals waste so much time eating, sleeping, breathing, it just gets dull. So a deity could decide they've had enough and just wander off to do something exciting.
This isn't what I signed up for...
At the other end of the spectrum is the deity that never gets picked. Why would a leader that wants health and prosperity for their kingdom want to merge with Ralph, God of Swamps and Decay?
But Ralph was chosen... And now Ralph to do what? Sleep? BATHE?! Sure, siring an offspring (see below) was fun, but all those years of pacing just to put a welp to sleep? Ralph used to have fun, and wander the cosmos. Ralph was in charge of entropy, and now they have diaper duty.
I'm surprised deities last the first year of a leader's rule.
You were inhabited by whom?
The previous leader was inhabited by Ralph. During their merger, the leader sired a son whom became the next ruler. That son, Stephan, wants to bring art and beauty to the realm and chooses Mina, Goddess of Beauty and Fashion.
A few years into this joining, Mina finds out that the father sired their host while having "Swamp boy" in their body. That's disgusting! Mina would never be associated with some MORTAL that was tainted by the likes of them. She will not inhabit them a moment longer!
As premised, each deity is in charge of something. There is no God of lounging about.
Well, sometimes, there could be a problem that needs their undivided attention. Tara, the Goddess of War, will need to oversee when a confrontation grows in size. Kevin, the God of the Hunt, will need to help across the land if there is an especially harsh winter when everyone is staving and needs to find food.
These tasks may be too hard when contained within a mortal body. More so if the body only cares about the well being of people in their immediate vicinity. If Stephan, learns that the enemy of the kingdom across the water is starving, then he would likely decree to let them starve, we need the God here with us. But Kevin serves all people and will need to leave Stephan in order to help everyone, else they lose dominion.