Reliance on a heart monitor can seriously damage your performance:
"....Don't worry about your heart getting tired
Basically, your heart is pretty much along for the ride. It will do what your leg muscles tell it to do (within limits, of course; the legs can't tell the heart to beat faster than max heart rate, for example). If your heart's been whacking away at 93 per cent of max for a good deal of time, it will never shout down to the leg muscles, 'Hey chaps! You've been pedalling (or scampering) for long enough. I'm getting tired, so will you please slow down?'
In fact, your legs will become fatigued far faster than your heart does. The heart will slow down if the leg muscles slow down, not the other way around. That's why the focus of your training should be on your leg muscles - that is, on the pace created by the leg muscles. Your goal should be to develop greater fatigue resistance in those leg muscles at your desired running paces or cycling speeds. You don't have to worry about the heart getting fatigued: that old fellow can pound away at high rates for long periods of time. Your leg muscles are your weak link...."
Lots of cycling articles (and other endurance sports)