Well, I have a question for you, 1.) was your Tamagotchi a baby or toddler when it started to get sick a lot? and 2.) when it was sick, did he/she have a lot of little poopies around him/her?
Because what I've noticed on almost every single Tamagotchi that I've owned, when they are Babies and Toddlers they tend to get sick very easily, I left my Music Star alone for about 15 minutes with one poop and he got ill, then again he was ill as a child with nothing around him. Actually, I think that as a baby baby, the Tama get's sick automatically, like a care need, testing you or something.
Also, if you leave the Poopies out on the screen to long, your Tama will get sick no matter what, like this morning I woke up late and Tarakotchi (my Music Star) and he had three little Poops and was ill. It took two doses of medicine of make him better.
If you Tama is an adult, however, I'll not sure, so get back to me, and I'll look over the internet and try and help you as best as I can. I apologize if this is useless information, but I really hope that this helps even a little for you.