Can TheAuctions.ca reopen an auction if I want to make a higher bid?

No. Once an auction is closed, and the final bid exceeds any reserve price, no additional bids will be accepted. If an auction hasn't reached its reserve price, it is still not a guarantee that you can make a new bid, as the seller can still choose to sell to or negotiate with the existing bidder(s).

It is advisable to place your bids earlier in the process, as any last minute bids will still extend the auction.

Note that once an auction has opened for bidding, traditional offers will not be accepted.