Is it possible to be diagnosed with epiglottitis more than once?

Possible but...: Epiglottitis became a rare disease entity since universal hib (hemophilus influenzae type b) vaccination has been instituted in early 1990s. Rare cases of epiglottitis seen last decade were caused mainly by s. Pneumoniae or group a streptococcus.

It is uncommon: Repeated episodes ("recurrent") epiglottitis is uncommon in adults. The published literature suggests that it can be caused by problems with the immune system. You may want to discuss this possibility with your doctor.

Rare: When recurrent acute epiglottitis occurs in adults, it is important to investigate the immune system because a quantitative or a specific antibody deficiency could be found. Same probably holds for adolescents and children.