Just got a call from my FFL that one of the 5 cans I bought in September last year was returned as "Inconclusive".  I have three of them that were approved in March, and one still pending.  Anyone heard of this?

There's no such thing, your stamp is either approved or disapproved. Ask to see whatever paperwork he has from the ATF, I'm betting it was simply disapproved because of an error on the paperwork.

Just spoke with Emma at BATFE and she stated that it was disapproved due to inconclusive FBI background.  She has my other can as well and it’s still pending.

She was unable to state why, and gave me the FBI checks website to challenge it.

Ask to look over the paperwork, make sure your dealer didn't misspell your name on the form 4 or anything like that. Same goes for the fingerprint cards.

"Inconclusive background" can mean the FBI found something that needed more info on, but didn't get it.  Most common is there is a record from a LE agency, but no final outcome.  So the FBI would ask the agency for more info, and if they don't respond, the background check is "inconclusive".   Since this is for NFA, the NICS rule to transfer after 3 days with no conclusive results does not apply, so FBI tells NFA branch the BGC is inconclusive, and the Form 4 is disapproved, and stamped in red "disapproved" or "return without action."  I have seen both on red stamps on disapproved forms.

This is an ongoing issue, plenty of threads about it in the past.

Due to backlog, they are not actually running your prints for a background check, they are running a NICS check. If it comes back delayed, they wait XX days, and if not resolved you are denied.