Bettas can be very finicky about food, but they don't tend to die of starvation. Eventually you find something he responds to, or you keep feeding him the rejected food until he accepts it. Or you can fast him for a couple of days and then feed.
Please don't give up on keeping bettas. You've had some bad luck of late, and luck is beyond anyone's control. All lifetimes are brief--some people refuse to have any more pets because it hurts so much when they die. I don't subscribe to this view, however. Fish diseases are notoriously difficult to treat; you will see advice here on formulas to obtain just in case your fish might get gravely ill some day, because what is available to treat them at pet stores is inadequate. This may be, but some conditions defy our attempts to understand or accommodate them.
SO I for one would continue to keep my eye on the Fluval Chi.