Stamina takes awhile to build up, and you have to do it correctly or you could hurt yourself and or regress the stamina. So the best way that I know of to build stamina is to build yourself up slowly to be able to ride a 100 miles in a day, thus you need to follow a century training schedule, like this:
http://www.kintera.org/htmlcontent.asp?cid=54755
If you are having trouble going say 1 mile then you need to add 4 weeks to the beginning of the schedule, so the first 4 weeks would look like this:
Week 1; Mon 1 mile; Tues 2 miles; Wed 3 miles; Thurs 0; Fri 2 miles; Sat 5 miles; Sun 2 miles.
Week 2; Mon 2 mile; Tues 4 miles; Wed 5 miles; Thurs 0; Fri 4 miles; Sat 10 miles; Sun 4 miles.
Week 3; Mon 3 mile; Tues 5 miles; Wed 6 miles; Thurs 0; Fri 5 miles; Sat 15 miles; Sun 5 miles.
Week 4; Mon 4 mile; Tues 6 miles; Wed 8 miles; Thurs 0; Fri 6 miles; Sat 24 miles; Sun 6 miles.
Then week 5 is where week 1 begins on the chart.
When you do this schedule DO NOT try to go further then what the schedule says regardless how easy it seems, the purpose of the schedule is to build up your stamina without getting hurt or burned out. Also at this time disregard the easy, pace and brisk stuff, all you want to do at this time is put miles under your belt in a controlled fashion, once you've done your first casual century then you can go back and start over with the schedule week 1, not the week 1 I created, and pedal easy on easy days, pace means a speed a bit faster the easy but try to keep it steady, and brisk means you pedal faster then pace. Once you get use to that you can start over again...crazy as all this sounds, and add in intervals every other day which are tougher than brisk but it will make you a faster rider as the weeks go by so then you have stamina plus speed! You can google bicycle intervals to see how that works or post back here and we can lead you through that. The above schedule is more for people under 50 years of age, if you're older than that then you may need more then one day off a week for recovery especially above 60; if you are older you can try the schedule as is but if you find yourself worn out then respond to this post and I can rework the schedule to include 3 days off but the time it will take to get to 100 mile point will take a bit longer but you will still get there. When you're older it takes more time to recover so you need to pay attention to your body so you don't overdo and hurt yourself.
I hope that helps and works for you, it should, I've given that plan to friends of mine who complained about the same issue as you have and those who actually followed it through to the end saw major improvements and were quite shocked as to how well it worked for them.
The very last thing I recommend, if you haven't had it done lately, is to get a heart stress test done before you try the schedule I posted to make sure your cardo system is in good shape and can take the load you're about to put on it. PLEASE do this first thing so you can rule out any heart issues (regardless what you think, you are your worst doctor!) so you don't have a heart attack on the bike and maybe die from it. Make sure you tell your doctor you want a stress test done because you are going to be riding a bike for exercise and you are currently having stamina problems and want to make sure it's not heart or lung related problem before you proceed any further.