Oh my.. Well first off you got VERY lucky with the dropsy because I never would have done that treatment and dropsy is almost always lethal anyway. At least we know it's entirely bacterial.. which is what I would have guessed anyway. It must have responded to the neomycin and maybe epsom salts.
So I think we need more info: http://www.bettafish.com/showthread.php?t=49233
But I'm pretty sure this is all going to apply to you..It really sounds like water quality issues and overfeeding/poor feeding issues.. maybe temp issues..
Bettas need to be kept in 2 gallons minimum. In these twice weekly water changes of 50% and 100% are needed. Bettas kept in 1 gallon containers live an average of about 2 years compared to double that+ in larger containers. The 1 gallon would need 3 weekly water changes of 50%, 50% and 100%, and even then they will be subjected to ammonia.
The 50% changes the betta can be kept in the bowl and use a turkey baster to remove half the water and as much of the debris as possible. For the 100% you need to remove him - scoop him out with a plastic solo type cup and set aside while you thoroughly rinse the bowl and gravel to remove the debris. Then he should be acclimated to the new water by floating for an hour while you slowly add a couple tablespoons of new water to the cup every 10 minutes. When you release him, try to let as little of the old cup water back into the tank as possible. All water changes should use same temp water, matched to running tap using the in tank thermometer and the water needs to be premixed with conditioner before adding it to the betta tank. If you don't already have anything, you can use gallon water jugs from the grocery store - rinsed thoroughly in hot water but no chems.
Most people will tell you that you can't ever fully cycle a less than 5G, despite your filter, and you will alwys need these changes.. you can try, but careful daily monitoring and reliable test kits should be used. This is for something 2.5G. Anything else is pointless, and actually stresses your betta because there is no way for him to get away from the current created from the filter.
Bettas are tropical fish and must be kept at a temp between 76-82, with 78-80 being ideal. The temp must be stable and not be dipping or jumping around. In a 2 gallon you can get an adjustable 25w heater. Any new heater should be tested for 24 hours in similar size container with in tank thermometer to make sure it will hold a constant appropriate temp between 78-80F. Then the betta must be acclimated to higher temp either by floating in a cup inside the main already fully heated tank for an hour, or by adjusting the heater to increase the temperature of the tank no more than a degree per hour and 5 degrees per day.
Flakes aren't good nutritional value, and especially with something this small they muck up the water quickly causing excess ammonia. You should look for a good quality pellets whose first two or three ingredients are whole fish, not fish meal or wheat. He should be fed two small meals a day (how many depends on the pellet you pick up) and one fast day a week.
Right now it is imperative you keep his water really really clean. I would remove the filter and start 50% every other day changes and 100% once a week changes. I would add epsom salt at 1 tsp per gallon, predissolved. Leave it in there for at least 2 weeks. Along with this I would fast for the next week at least and also use an antibiotic like Kanaplex or Triple Sulfa.. I will tell you how to use it when you tell me what you got.