Can you re-issue a Payment Notice?

Yes inside the 5 day window, no after it. A Payment Notice is the payer's statement of the sum it thinks is due for the round, and within 5 days of the Due Date, the date the payment obligation is fixed, the payer can serve a corrected one, clearly marked as replacing the first, and the corrected figure stands. Once that window closes nothing can be repaired, replaced or backdated: a correction on day 6 counts for nothing, and the notice served in time, or the payee's application if none was, fixes the Notified Sum, the amount that legally must be paid. If the mistake made the sum too high, a Pay Less Notice in its own later window can bring it down. If too low, the notice binds for this round and the shortfall is picked up in the next round's valuation, the running pricing of the work.

A surveyor serves a Payment Notice for £90,000 on day two after the Due Date, then spots on day four that she double counted a £10,000 item. Still inside the 5 days, she serves a fresh notice for £80,000 superseding the first, and £80,000 stands. Had she only noticed on day six, the window would be shut, the £90,000 notice would hold for this round, and her route to claw back the £10,000 would be a Pay Less Notice in its own later window. Had the error been too low, say £70,000 when £80,000 was earned, the notice would still bind and the missing £10,000 would come through in next month's valuation.