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It is the way that Date Reservation widget works. Once a date is picked it is counted as reserved and it becomes unavailable for further submissions.
I have navigated through some other widgets but I was not able to find one that works in a way that you'd like to use. The only work around I can think of is to use simple Dropdown fields and enable the multiple selection feature with days and months are configured. I know it is not fancy and easy compared to selecting dates from a calendar. However, please let us know if you'd want set it up that way.
Do contact us again if you need any further assistance.