For how long does one have the right to say "patent pending" after submitting a provisional patent application in the United States?
There is a $500 per incident penalty for false patent marking. If a application is no longer pending then it would be a false marking to mark newly produced items with that mark. Of course you can file a non provisional at the end of the year or even another provisional application.
I don’t know if there is a legal aspect, but for me you have a patent pending if you have an active application in process. From the USPTO site.
A provisional application for patent has a pendency lasting 12 months from the date the provisional application is filed. The 12-month pendency period cannot be extended. Therefore, an applicant who files a provisional application must file a corresponding nonprovisional application for patent (nonprovisional application) during the 12-month pendency period of the provisional application in order to benefit from the earlier filing of the provisional application
So for provisional applications that would be for one year from the filing date. If you followed up with a non provisional application you could continue to claim patent pending until a patent is issued or until the application process ends for any reason such as rejection or abandonment.