How long should someone wait between transferring two $10,000 amounts to the U.S. to avoid reporting issues?

The US does not have such a rule per se. You can at any time request a SWIFT MT-103 Message Confirmation from the sending party to find out the exact status of wire. It could very well be that there is a correspondent bank being utilised and/or the information provided in the wire is not complete for the end settlement into the Beneficiary's account, etc.

The MT-103 message you then provide to your bank and ask them to trace the wire.