InfoPath Dev

I would first check the Internet Explorer settings, to make sure that your site is set to Local Intranet.

If that doesn't solve it, I would try to test further and see if there is a pattern. If it's a specific browser, or a specific OS, etc. Remember that there is one thing that changes in your environment even if you don't change the forms, and that's Microsoft updates. We could be talking about updates at the server level or at the machine level, on SharePoint or on the browser or on InfoPath. It's hard to tell at this point. But dig deeper and let us know what you find.

The Infopath browser form can be tried to be opened also in local Infopath Filler instead of in browser through Sharepoint Server's Infopath Form Service. And opening in In Filler, AFAIU, requires Full Trust and code signing but instead of informing so directly (in plain English) the error tells this equivocally:  

• Forms that require the domain permission level contain features that access information on a network, such as data connections, linked images, and code..  

Are you using certificates for code signing, which and how?
Self-signed certificates expire in one month.
If you run your own CA service or use 3d party CA certificates to digitally sign your code then there are a lot of possible issues to check . First, I believe, they are to be renewed once a year. Though, you would have got another and more direct error on this. 

If you do not use Infopath Filler/client forms, then check that your browser forms are not being tried for opening locally

Update:

Just as an afterthought, I do not have an access to Sharepoint central administration to check, but do administrator-approved forms havean option for expiration period of administrator approval? There is all the sense for its existence and it would be illogical if it does not exist with default expiration period (vs expiring by default certificates, passwords, etc.)