If you are eating very little, but are not underweight, can you lose your period?

Yes. There are two issues. One is critical body weight and hormone production. The other is body energy. So decreases in food intake and extreme exercising even in the absence of weight changes can drastically affect body energy, metabolism, and affects your brain's hormones and thus ovulation.
Typically no. If you are having normal weight (or I would say normal bmi), it will be hard to argue about a connection between your absent periods and weight, however, what is precipitating your decreased appetite may be a contributing factor (stress, depression). On the other hand and as with any menarchal women, a pregnancy test is needed to rule out pregnancy. Please talk with your doctor if further testing.