Hello Hannah,
I suspect this may be by design. When you purchase user spaces, though your purchase does have an expiration date, technically this is just adding to a "pool" of users in ArcGIS Online.
Let's say you start with 5 "Creators" that expire 12/1/19. You buy another 3 "Creators" that expire 11/15/20.
You will then have the room for 8 users. Those users aren't assign expiration dates based on when you added them, but when 12/1/19 rolls around, it's up to you as the administrator to decide which 5 of your 8 users you want to remove. That could be 2 old users and your 3 new users, 4 old users and 1 new user, etc.
I don't think it'd be unreasonable to ask to be able to see expiration dates of user spaces in ArcGIS Online, but I don't think they'll tie users themselves to expiration dates. I'd recommend posting it on ArcGIS Ideas so you can get some traction and additional supporters! Here's the link for that section of GeoNet: ArcGIS Ideas .
Thanks!
Rachel G
Esri Support Services
Rachel Guttmacher
ArcGIS Online Technology Lead
Esri Support Services