How frequently should I remove my pessary and clean it?

Daily if possible. Some pessaries are "user friendly" and can be removed by the user herself on a daily basis. Others are shaped such that insertion and removal by the wearer is most difficult, requiring trips to a clinician's office for periodic removal, inspection, examination, cleaning and reinsertion at 1-4 month intervals.
Depends. Ideal is about once per week and leave it out overnight. Some ladies develop discharge and like to clean it more frequently. Too frequent changes and the vaginal opening can become irritated. Some of our older ladies who cannot take their own pessary out are seen in the office only every 3 months and do quite well. Postmenopausal women do better w/ pessary if using topical estrogen.
Try vinegar Douche. Since prolapse affects many older women who have difficulty removing their pessary to clean it, many years ago I came up with an idea where if she is bothered by discharge she can simply douche with vinegar & water not more often than once a week. She should have a pelvic exam with pessary removed & cleaned by her gynecologist once a year, sooner if any bleeding or problems.