Question: Do we have to retain EOBs for a certain period of time?
Answer: Many practices retain EOBs for up to seven years — a nuisance, but they come in handy if a payer does a retrospective audit and demands thousands of dollars in refunds (believe me, it happens). The IRS also might like to have a look. Take a look at what your contracts do or do not specify on this point.
That said, there is no reason to keep the paper. A well-scanned version is just as legitimate — and easier to find later on. Just scan and store them by numerical assignment or whatever filing method works for your biller.