Ok.. using a single backup a day at low usage time on the internet is going to help.. but the internet connection can go down.. and not recover.. when that happens the backup stops with inprogress file half finished. This will at least bind up the TM backup until the next time.
You can manually fix it.. see A10 here. http://pondini.org/TM/Troubleshooting.html
However it can also happen at critical point where the actual files are being sorted into the backup.. TM is a very complex backup mechanism and there is a lot of to and fro between client and backup .. and over internet this can be corrupted easily.
I also think encryption makes this 10x worse.
I am just not sure where the encryption takes place.. ie is the TM sending encrypted info .. that would be difficult..
Or is the encryption taking place on the final step of adding the files into the backup..
Pondini says you can encrypt an existing backup on a local drive.. but not on a network drive.
http://pondini.org/TM/31.html
Here is where the details are above my paygrade.. why the difference??
If it can encrypt a local existing backup where is that taking place.. on the local drive.. ?? But it cannot do it on network because??
Having a remote backup is excellent.
Using TM is less than excellent.
I use Carbon Copy Cloner. It is rsync based.. whatever you use I think using something based on good old unix command line utility like rsync is the way to go..
But I have no experience with it over internet..
Doing a local TM backup and a remote CCC backup would be worth a try.. It is easy enough to check if the backup works...