This isn't strictly a maintenance issue, but of everything that can mechanically go wrong with your race, it's this lowly, lo-tech part that's likely to cause you to pull your hair out.
Why? Because companies that sell handlebar tape sell the plugs as part of the tape package, and while I love all the handlebar technologies available by companies like Profile Design and Cinelli, both suck when it comes to the handlebar plugs included in those kits.
Frankly speaking, use Profile or Cinelli handlebar tape, but throw the useless plugs away. The reason really isn't safety as much as legality. You put your bike on the roof rack, travel to the race, and take the bike off the roof and put it in the transition area, not realizing your cheap plastic handlebar plugs have popped out. Then, during the swim, USAT marshalls are patrolling the racks, looking for those profligate cheaters who're daring to sneak through the race with plugless death machines. You get out of the swim and, whammo, you're DQ'd before you start.
The solution is simple, and it may cost you $2, and if you're really a big spender it'll cost you double that. The cheap version is the metal plug shown here, and this particular one is made by Kool Stop. I pay fifty cents (excuse me, I understand nowadays it's pronounced "fitty-cent") per pair, and giving your LBS the benefit of the margin doubt, no way you can pay more than $2 per pair (I pay fitty-cent because I buy these by the 55-gallon drum). Maybe a buck a pair is more like it. These spring-loaded plugs are much more resistant to popping out of your bars.
Then there's the high-tech, several-moving-parts style, which includes a rubber plug that, when you screw in the bolt, squeezes and wedges the rubber into your bar. These plugs absolutely can't come out.
These are made by Velox, the same folks who make other unsexy stuff like the rim tape for your wheels that keeps you from getting a flat. These plugs come in a card, as shown, so the next time you wander into your LBS look for this card and buy these plugs. They cost me $1.30 per pair (I buy them by the pickup truck load) so at most you'll pay, I figure, $4.
Yes, you can wrap several laps of black plastic tape around the piece-of-chit plastic plug, but they'll still eventually come out, probably just before your season's most important race.