From the T&Cs
4B.2. An "Eligible Stay" is one or more consecutive nights at the same Participating Property, whether or not you checked-out and checked back in, during which you paid an Eligible Rate and presented your Preferred Guest number at registration. An "Eligible Night" is each night during an Eligible Stay. All stays are deemed to occur on the date of arrival; however, nights within a stay belong to the month in which they occur.
Couple of examples:
25 x 1 night stays would qualify on stays. (25 stays, 25 nights)
10 x 5 night stays would qualify on nights. (10 stays, 50 nights)
Hope I haven't confused you more.