If you live in a motel/hotel for more than 30 consecutive days, or you clearly show an intent to remain for a longer continuous period than 30 days, then your situation falls under NRS: Chapter 118A, which governs the landlord/tenant relationship. (This relationship is also pursuant to a rental agreement, whether written or verbal -- hence the feedback we received from Four Seasons in the QoD to which you refer, which ran on 2/27/2013, who said that they're more than happy for a guest to stay for longer than 30 days, but if you wish to, then you're required to sign a contract with their sales office, as opposed to merely transacting through the hotel front desk.)
As you'll see, should you choose to click through the above link, NRS: Chapter 118A is a pretty long document, with multiple clauses and sub-clauses, so we'll just cover a few of the pertinent points here and leave you to peruse the rest at your leisure, should you require more in-depth information.
One of the fundamental rights afforded to a tenant, as defined by the statute, is the right to occupy a dwelling unit to the exclusion of others. Your landlord is also obliged to keep the unit "habitable," which includes providing "essential services," i.e., heat, running water, hot water, electricity, and gas. Those are the basics; if your rental agreement covers other services, such as air conditioning, then those services are also deemed essential. As of October 1, 2011, a functioning lock is also considered an essential service.
If it's not addressed expressly in the rental agreement, then the landlord is obliged to provide maintenance and waste-removal services, without charge. Similarly, it's fine for the tenant to have children and pets in the dwelling, unless otherwise stated in the agreement.
A tenant has the right to display the flag of the United States in certain areas, subject to certain provisos (see Clause 118A.325 for details).
While flying a flag out of your window (if you're in one of those rare Las Vegas hotel rooms that has an opening window), or housing a herd of goats in your suite, would likely be frowned upon by most hotels (a dog, maybe, but even cats are distinctly unwelcome), it's presumably the areas of rental-payment and possession-rights that are the crux of the casinos' fear of any guest extending his or her stay. This is because basically, the onus is on the landlord to get rid of a non-paying guest, and legally they can't do that by, say, changing the locks, or cutting off your water supply, or banging repeatedly on your door in the middle of the night. If you refuse to leave and/or pay, the landlord must take you to court in order to recover overdue rent, plus any monies owed for damages, or to evict you (see NRS 118A.470). We all know how court cases can drag on and on, especially when the tenant "may defend and counterclaim for any amount which the tenant may recover under the rental agreement" (see NRS 118A.490). Hence, motels and hotels in Las Vegas just aren't going to take any chances.