There are two options, you could put your formula inside an IF statement 
=IF(SUMIF([ABFOUT.xlsx]ABF!F:F,B2&"*",[ABFOUT.xlsx]ABF!O:O) =0,"",SUMIF([ABFOUT.xlsx]ABF!F:F,B2&"*",[ABFOUT.xlsx]ABF!O:O))
which returns a blank if the result is 0.

Or, you can use Excel Options>Advanced>Display Options for this Worksheet and uncheck "show a zero in cells that have a zero value"

Can you use either of these?