Canada Border Services Agency has provided a response to the following question.
Can the same goods be subject to surtax more than once? For example, goods that are imported into Canada and which have surtax applied are then returned to the US. Drawback is not claimed and the same goods return to Canada. Are these goods subject to surtax a second time? If they are not, how is that indicated on the release request?
Yes, it may be necessary to pay the surtax twice on goods that are re-imported into Canada for a second time.
Per paragraph 8 of Customs Notice 18-08 respecting The U.S. Surtax order, goods of Chapter 98 and 99 (including certain goods eligible for the Canadian Goods Abroad program) are not excluded from the application of surtax. Thus, any goods imported temporarily (having paid the surtax once) and subsequently exported  will be subject to the surtax a second time upon re-importation. There is currently no incentive program or other method to relieve this legislative obligation to pay twice.
However, if a Drawback was claimed and granted on the initial importation and subsequent exportation, a drawback/refund of the surtax may be available (thus, the net effect is to pay the surtax once).