I'm sharing my original problem and then resolution here.
Originally, I was only passing in the ACTINDX value:
<taPopRcptLineTaxInsert>
<VENDORID>ADVANCED0001</VENDORID>
<POPRCTNM>RCT1549</POPRCTNM>
<TAXDTLID>USCITY+PS1N0</TAXDTLID>
<TAXTYPE>0</TAXTYPE>
<ACTINDX>169</ACTINDX>
<TAXAMNT>0.91</TAXAMNT>
<TAXPURCH>90.25</TAXPURCH>
<TOTPURCH>90.25</TOTPURCH>
</taPopRcptLineTaxInsert>
Although I passed in a value > 0 for the account index, 0 appeared for this value in the POP10360 table and it would not post.