Looking on the internet deeply has found these results:

their reelection is the most popular phrase on the web.

their reelections 112,300 results on the web	their reelection 165,600 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Sarah Louise is running for reelection. Taking a hard line against criminals is a platform for his reelection. Senator Howard lost his bid for reelection. You wouldn't have won reelection if their PACs hadn't dumped 10 million into your campaign. Hardison tells me he runs a lot of gray money through his reelection campaign, so he'll take the bribe out of his reelection funds. Walker needs the state for reelection... I'm running congressman Murray's reelection bid. Hunt funded Grell's reelection campaign.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

their reelections

112,300 results on the web

their reelection

165,600 results on the web

More popular!

Sarah Louise is running for reelection.
Taking a hard line against criminals is a platform for his reelection.
Senator Howard lost his bid for reelection.
You wouldn't have won reelection if their PACs hadn't dumped 10 million into your campaign.
Hardison tells me he runs a lot of gray money through his reelection campaign, so he'll take the bribe out of his reelection funds.
Walker needs the state for reelection...
I'm running congressman Murray's reelection bid.
Hunt funded Grell's reelection campaign.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.