What would be reasons why a conservator would want to limit or prevent visits to a dementia patient?

Dementia: Seeing a lot of people sometimes can make dementia patients more confused.

Welfare of the pt.: Usually this is a determination made by the doctor rather than by the conservator, but they may have the right to make that call also, depending on the law in your area. Generally this is done when it is deemed not in the patient's best interest, e.g. If the patient gets agitated or endangers themselves or others when that visitor has been there. Hope it gets better & you can see your visitor.

For example: If a conservator determines that the visit is not in the best interest of the patient, that is one possibility (eg to avoid unnecessary stress, or after the patient requirement).