The bid countdown on your computer is not the official eBay countdown, and just because you do not see a bid at the end of the auction does not mean that eBay did not receive a bid before the auction ended.
Signals do not propagate infinitely fast, so at any given time the information shown on your page may be a few seconds out of date compared to the info on eBay's servers. Even when your countdown reaches zero, there may be valid bids that have been received by eBay but that have not had time to be displayed on the bid history page or listing page.
You should always assume that there will be other bidders bidding against you. Many bids are placed towards the end of the auction. If your strategy relies on being able to counter late bids, it is time for you to get a new strategy. No one can guarantee getting the last bid; in many cases you may not be able to place a second bid at all, so make your first bid count: bid your maximum amount, once.
If you are interested in winning an item, your best course of action is likely to decide in advance the maximum amount you are willing to pay for the item including any taxes or shipping, and then bid the appropriate amount once, as late in the auction as you are comfortable with. If the amount is a round number, consider adding a few cents to avoid a tie which would go to the earlier bidder. Bidding late ensures that other bidders have little time to react to your bid, or to bid you up and possibly discover your maximum bid amount and then retract (if a shill) or outbid you (if a competitor).
Because of the way eBay auctions work, there is no real benefit to bidding less than your maximum amount. Bidding less will not allow you to pay less -- except possibly by a minimal amount in rare cases where you outbid the underbidder by less than a full increment and wind up winning; in that case bidding your maximum may result in paying one full increment above the underbidder's bid. But the downside of bidding less than your max is that a late bid can beat you and you can lose for an amount less than what you were actually willing to pay.
If you bid your true maximum and the bid goes through, the only way you can lose is if someone else is willing to pay more, and they actually place a higher bid before the auction ends, or if someone was willing to pay the same amount as you and they bid sooner than you did.
Some bidders bid for a bargain, hoping to win; veterans bid to win, hoping for a bargain.
