Plesk has a habit of getting itself into a bit of a mess and nothing can be more annoying than it disabling some of your websites and then outright refusing to let you re-enable them. You may find, due to some reason or another, perhaps a failed backup, resource issue or manual suspension, when you try and reactivate a domain, Plesk simply refuses, either with an error message such as:
Error: Unable to activate the domain: The domain is suspended.
... which is not helpful as it simply makes no sense. If it wasn't suspended then you wouldn't be trying to reactivate it!

Regardless of whether you get a more specific additional error message or not, you will see this message when you try and reactivate the domain if Plesk has broken itself:
Error: Some of the selected domains or aliases were not activated.
Not helpful.

Luckily the fix is pretty simple, but it's a shame it has to be done at all. To fix a domain that is "stuck" in the suspended state, run this from the command line on the server that is experiencing the problem:
/usr/local/psa/bin/domain -u example.com -status enabled
... replacing "example.com" with the name of your stuck domain (or sub-domain) and "/usr/local/psa" with the path to your Plesk installation (this should already be correct for most people).

The domain(s) should now show as active again once you refresh the domains page in Plesk.