Take a look at all angles.
Equipment. Do you have good wheels and fast tires? Are your tires always properly inflated.
Aerodynamics. Are you sitting upright or are you leaning? Does your bike fit? Are you carrying panniers or wearing flapping loose clothes?
Nutrition/Hydration. Do you fuel and drink correctly before and during rides? How's your blood sugar?
Recovery. Do you get appropriate rest between rides?
Measuring. Do you have a heart rate monitor? Do you know what kind of power you produce? Cadence meter?
Engine. Are you carrying extra bodyweight? How's your cardiovascular fitness? Are you on medications?
Training. How hard do you push? Are all your rides at the same pace? Do you do short rides at time trial pace?
I had a pretty good increase in speed during my 3rd year back on the bike age 55. During 2010 I struggled even on short rides at 11mph. I wanted to try a century but couldn't meet time constraints (and in TX I did not deal with the heat well enough to be exposed that long). This year I improved on the points above and have done some 50 mile rides avg 15mph. I can't pinpoint one exact thing, but I have changed these aspects:
* Rode fewer miles and got more rest between rides
* Lost 25 pounds. Less weight, easier breathing, handle heat better. Still many # to go.
* Changed tires to 23c fast tires (had 25c bulletproof tires w/ liners)
* Got a camelbak as I have great difficulty using a waterbottle while riding .: less dehydration and not having to slow down to drink
* Changed pre-ride diet to get blood sugar higher and found a sports gel that works for me. Probably borderline low blood sugar had a LOT to do with lack of speed.
* Changed to slower cadence -- not everyone is designed to spin smooth at 100rpm without blowing up
* Found that I can generate a lot of torque during part of the pedal stroke. The more I stomped, the stronger my legs got.
* Got a heart rate monitor to see when I needed recovery and to see when I was overdoing it.
* Stayed healthy and able to train consistently for most of the year. No long downtimes.
We have a 77-year-old in our bike club. He used to be a runner and started riding a bike 2009 when his knees told him to quit running. He had to take a long hiatus after a nasty bike fall (broken neck vertebrae, got several plates/screws) last year but he's back on his road bike hanging with the strong 50-year-olds including the climbs and on the hottest days. Very inspirational.