If you are talking a block of days without any breaks you need to check with the hotels to see what the local laws are for long stays. In many areas, after some number of days (usually 30) you are no longer a hotel guest but a resident.
The advantage to you or whoever is paying the bill is in most areas, there is no hotel tax on residents, and in many cases, there is some procedure in place where you can sign a form or whatever so that you don't have to pay it on the first 30 days.
The disadvantage is it may not count as a stay at all and you don't get any credit. It all depends on what the local law is which could be at the state or even down to the local level.
To maximize points, I would be hotel hopping on a regular basis. Breaking the stays up will quickly move up the number of stays and any bonus points they are offering at the time.