How to make my betta happy?

Your filter is home to the majority of the beneficial bacteria that are cultivated during the nitrogen cycle. As soon as you turn it off, the bacteria starts to die. Kept off for prolonged periods it will kill your cycle and can lead to unsafe parameter spikes.

Your filter needs to stay on always.

Bettas prefer a gentle current. It is best to use a filter with an adjustable flow control and to set the filter flow to low, as they are not very strong swimmers. Another good option is a sponge filter. If your current filter is too strong, you can remedy it by covering the intake with a pair of pantyhose, putting a tall plant in front of the output, or follow these instructions to outfit your filter with a simple current/flow reducer: http://www.petfish.net/kb/entry/347/

However, unless this is a new filter, that's not likely the problem.

Troubleshooting should start with a test of your water parameters. If you don't have a test kit, most LFS and many pet stores will test your water for you.

Be sure if you have a store test it that you get exact readings from them. Don't settle for "it's pretty good" or any such vague answer.

Test at least for Ammonia, NitrITE and NitrATES. (Ammonia and NitrITES should be at 0ppm, NitrATES under 40ppm, preferably well under.)

Also, what is the temperature exactly? 80 degrees is good for Bettas. If the temperature is under 78 degrees for any length of time it will negatively affect him, and over a long period will lead to lethargy/loss of appetite/illness/disease/early demise.

Good luck.

If there is a filter on the tank that disturbs the waters surface I don't believe he will blow a bubble nest. Maybe try getting a shrimp or two for tank mates that might catch his attention. Not sure what else would cause this... maybe age? Good luck hope you find a way to cheer him up.