I've met a fair number of travelers who remain at the same hospital for years. Really it is up to the facility. However, as soon as you work over one year in the same area (even at five different hospitals), or sign a contract that takes you over one year, that becomes your new tax home on that day. Since a good bit of your take home pay derives from the tax benefits of working away from home, it may not benefit you financially to travel to only one location. Becoming perm with staff benefits could be better with good health insurance (usually), PTO, vacation, holiday pay, and education.
There are a good number of agencies that are willing to pay those tax benefits forever, some with a mandatory trip home, others with a 30 day time out, and while those do protect the agency from the IRS, they do not protect the traveler. Those tax liabilities just pile up for as much as seven years and if you are audited, you will owe back taxes, penalties, and interest - perhaps as much as six figures in just a few years. It is not worth the risk in my opinion no matter the low audit risk (although the audit risk increases if the agency gets audited because of their own poor due diligence about tax homes).
You may already be in this position if you are not maintaining a residence you can return to at anytime at your tax home. This cannot be artificial, you have to have real ties to your tax home - ideally working there every year but it is not required if you have other real ties like your church, voter registration, spouse, historical place of residence, et cetera. If you don't have this, you are itinerant (without a tax home) and so everywhere you work is home, and you are subject to taxes on all your compensation, just like everyone else who lives there and is not working away from home on business. Nothing wrong with being itinerant, and it could be better financially in some cases. If it cost more than about $10,000 a year to maintain a residence, than being itinerant is the way to go.
If your tax home shifts to an assignment location you have been at for over a year or most of your income comes from there over a couple years even if you do an assignment somewhere else, then you will owe that work state taxes on all your income, just as you would owe your permanent tax home somewhere else as a traveler their share of all income earned anywhere. Itinerants only owe income tax to the work state, potentially saving money over someone with a tax home in a state with high income tax.