I’m on a shared host. The cron.php is running as the user I login as. Everything is owned by this user. I do not have root.
I noticed another issue that wasn’t happening before. In the emails that go out via email templates, the dates are showing as 2016-11-08. They should be, and previously were, 08-11-2016. That’s how I have it set in both Locale and my profile settings. Any idea why this would be?
It’s a pity we couldn’t get a listing of your broken permissions before you fixed them.
Basically, the problem I’m investigating happens when cron runs as a different user than the regular SuiteCRM app.
That would depend on your hosting provider, but normally the SuiteCRM app would run as the Apache user (www-data on Ubuntu, for example). If cron uses a different user (even if it’s not root) some files might be created in the SuiteCRM’s cache and then the application could have trouble getting write access to them. But that situation needs quite a lot of info to analyse: users, groups they belong to, owners of directories and files, and finally the permissions set on them.
(I don’t know about the dates problem. I recommend a Repair and Rebuild after the permissions reset).
I noticed that the SuiteP theme dir was drwxrws and a few dirs/files inside were similarly set. I’ve never seen the SuiteP theme till now and it’s pretty nice. There must have been some other perm issues because of what I was seeing even using the SuiteR theme. I’m glad I was able to resolve this with help from folks like you and the admins.
All files are user:user as far as I can see. I have a jailed shell so no root access to be able to see running processes. As a former Unix administrator, I find this very uncomfortable. 
But what can I do, costs a lot more for dedicated hosting with root access.
Can you see entries like this in your syslog (if you have access to it)?
Nov 8 18:28:01 SuiteCRM CRON[50766]: (www-data) CMD (cd /var/www/html; php -f cron.php > /dev/null 2>&1)
Don’t think I have access to syslog. This is shared hosting.
No problem with cron. It runs on the server.
Apologies for resurrecting a stale topic, but hopefully this will save someone else that finds this as the top result on Google:
I migrated through the appropriate packages from Sugar 6.5.9 to Suite 7.7.9, and somewhere along the way files got left behind in the custom/modules/EmailTemplates directory. Moving that dir to another location (strictly as a backup) caused the EmailTemplates module to work correctly.
I’m assuming that the content in custom/modules/ overrides the same content in modules/ , but please correct me if I’m wrong on that.
At any rate, this did solve my problem.