One reason they keep coming back may be that there are eggs that hatch after you've killed the adults. Another reason may be that ants keep bringing more onto your plant. Have you noticed ants around?
I like to use a spray of water to remove as many of the adult aphids as possible. For larger plants, or those growing in-ground, I use the garden hose. For my smaller container-grown plants, I just hold them under the kitchen faucet, or use the sink sprayer.
Once I've gotten rid of most of the adults, I spray the plant thoroughly with a soap solution. I repeat the soap-solution spray about every 7 to 10 days, in case there are any eggs that have hatched out. A series of 4 spraying usually takes care of the problem.
If ants are present, treat to get rid of them.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams