As per my understanding, you are restoring data from a week old content database backup file. For this, you are doing restore from backup file, unattach it and then recover your data.
first, you should be able to recover files/pages/list from end user recycle bin where data is kept for 30 days ( by default) after deletion. After 30 days, deleted items are moved to site collection recycle bin and stays there for 30 days more, by default.
So you should not need to restore database for 2 months from old content database.
You can also tune recycle bin to your needs:
http://www.mssharepointtips.com/tip.asp?id=1064 (It's written for 2010, but same concepts in 2013 as well).
To your question, there's not really a way to keep a week old content databases somewhere in same farm. You can restore you content database to different SP farm like QA/Dev one, mount it and then recover data from there. However, there is again no way to
keep that content database refreshed automatically. You should really look upon a strategy to divide your sites into different databases of smaller size to reduce backup/restore time.
Hope this helps.