I've got a chart that I think will help you figure out what Doc and Frenchie are getting at. If you've never seen one before it's a power/time curve. Everyone has one and while they are all shaped basically like this. How steeply the fall off is varies by person. Now, I must say that I generated my on my own, based on my training data (for long distance rides) and actually going out and seeing how fast I could hold a speed over a given time/distance (short distances/sprints). I took those numbers and plugged them in at kreuzotter.deespeed.htmOpen ↗ It's funny that the correlation numbers matched so closely. To have really accurate values, you really need a power meter (which I don't have).
Anyway, by looking at the graph, what you want is not more strength indicated by the maximum number one can hold for a very brief peroid, but more POWER at a given time say 30, 60 or 90 mins. Working on maximal strength will not really improve your power numbers at 30, 60 or 90 mins. Doing intervals and the other suggested techniques will.
Good luck,
Lonnie
EDIT: BTW, the time intervals in minutes are 0.2, 1, 6, 12, 30, 60, 90, 120 and 180. FWIW, my 1 min estimate might be low. I feel pretty confident about the other numbers (esp as the times get longer). Other rider details, I'm 140 and my bike weighs 21 lbs....