What can I advise a client when their refund shows as "Processing" 10 weeks after e-filing their return?

They need to be patient and wait.

Mention the refund is earning 3% interest this quarter.

The early bird gets the worm.  The early filer evidently doesn't get a worm, or a timely issued check but does get 3% interest --------------------------- someday.

I called PPS yesterday to inquire on 4 clients with same situation.   2 efiled/accepted February; 2 efiled/accepted March       3 of the 4 had a child in 2020 - so return has RRC credit.   The agent said all these returns are requiring a manual review. Says the IRS department handling these is behind so expect minimum of 10weeks before the return can possibly be released.   Could be longer if it is determined a letter needs to be sent to taxpayer.  

Made the calls as a courtesy to my clients - 2 of the 4 called yesterday inquiring if I had any news.  Clients are Amish so no access to a computer to check Where's My Refund.  

From the latest IRS update:

Including current year returns, as of April 16, 2021, we had 16.1 million unprocessed individual returns in the pipeline. Unprocessed returns include those requiring correction to the Recovery Rebate Credit amount or validation of 2019 income used to figure the Earned Income Tax Credit (EITC) and Additional Child Tax Credit (ACTC).

--Of course they're lying about returns requiring "correction" to RRC; a return with credit based on an added 2020 child is correct, but they don't believe you anyway.  

Make sure they don't have any debts or liens that would be able to take the refund. Get transcripts from IRS. Could also be identity problem.