I'm aware it's not a feature of Wordpress, but I was wondering if there was a way or a plug-in (haven't found one from searching) that allows me to force a user to change their password after a defined number of days.
I was busy writing up a plugin for this without even checking of one already existed. So I did a little research and found out that it does indeed already exist and that the path I was going down was the right one. Well, there's no need to reinvent the wheel here, so here's the link to the existing plugin.
Does what you need - I tested it myself.
Login Security Solution will also do this, but in my opinion it's not a good idea. If you force users to change their passwords too frequently, they're more likely to get frustrated and adopt bad practices in order to make things easier for them.
See these SE threads for more information: