Once you've placed a bid on an item, all of your current bidding activity can be viewed from the Members Area > Buying > Bids section. The default filter in this section will only include auctions which have not yet ended; and you can filter the default list using the filter drop-down menu to view only the items which you have been outbid on:

HipStamp: https://www.hipstamp.com/members/buying/bids
HipComic: https://www.hipcomic.com/members/buying/bids
HipPostcard: https://www.hippostcard.com/members/buying/bids

Additionally, from the filter drop-down menu, you can also switch to view auctions which have closed - specifically either auctions that you have won, or auctions that you have lost:

HipStamp: https://www.hipstamp.com/members/buying/bids/filter/lost
HipComic: https://www.hipcomic.com/members/buying/bids/filter/lost
HipPostcard: https://www.hippostcard.com/members/buying/bids/filter/lost