Thanks for your patience. I know that treating a flea infestation can be frustrating. Thankfully the flea life cycle is known and predictable. Taking advantage of that knowledge and applying good quality products will get your problem under control.
The most important thing to know about fleas is that only about 10% of the total population of fleas is actually on your pet, meaning that 90% are in the form of eggs, larvae, and pupae in the environment (your home and/or yard). It's important to wash thoroughly or toss bedding that your pet uses and vacuum frequently. You can place a flea collar in the bag of your vacuum to kill what you suck up.
The pupae that hatch out on to your pet are pretty much resistant to everything and they are very tough to kill, so they're usually the ones that make it through whatever treatment you do to the home. They also can stay in that stage for a very long time - up to two years, so just when you think things are under control they can spring up again. This is why it's important to be vigilant and use a good flea preventive like Frontline Plus or Frontline Tritak, Advantage, Revolution, or Comfortis monthly all year round if you've had a problem in the past. My favorite product in terms of "bang for your buck" is the Seresto collar made by Bayer. While it may be "sticker shock" at $65+, the collar lasts EIGHT months and works fantastically to kill fleas and break the life cycle. You can find the collar for various sale prices in stores and online. That cost of eight months of high quality flea prevention is quite cheap.
The pupae spring out into adult forms in response to vibration, heat, and carbon dioxide, among other things, so just walking around or running the vacuum will wake them up. My parasitology professor at vet school recommended vacuuming twice about an hour apart, once to wake them up and a second time to suck them up, so he put it.
Some of the spot on flea products like Frontline Plus, Advantage and the Seresto collar also have growth inhibitors that will affect the fleas' reproductive cycle, so they can be of added help in breaking the cycle in multiple places.
It's also really important to apply the flea preventive products exactly as described. They all have slightly different directions when it comes to how long before or after a bath they should be applied. They mostly all are 'water proof' however if you are bathing very frequently or with de-greasing soaps like Dawn, it may decrease their effectiveness of the product.
Also, keep a look out for other places that your pet could be picking up fleas, especially if he goes outside. This applies to you as well - if you visit a heavily infested home you can bring them home with you too. Fleas don't really like people but they will hitch a ride on you to get to a yummy dog or cat!
The life cycle of the flea lasts about three months from the time a female lays eggs to the time those eggs have gone through the cycle and hatch out as adults. This means that one dose of flea prevention that only lasts a month is not going to cut it. It'll work for a month and then when it wears off, the flea life cycle will keep on cranking. That's why I really like the Seresto collar for a long term solution. It's also of vital importance that all pets in the home get treated with a high quality product. If any pet in the household goes without prevention, the life cycle will continue to move forward and there will still be more fleas coming up.
Here is some more info on the flea life cycle: http://www.petmd.com/dog/parasites/evr_multi_understanding_the_flea_life_cycle
In a situation where the environment is heavily infested with flea eggs, larvae, and pupae, it's a good idea to also treat the environment - either by calling a professional exterminator or looking at products like flea bombs that will kill the eggs and larvae.
To give the short answer to your question - yes, it is possible to stop fleas! It just takes the right knowledge and the right equipment.
Hope this helps :)