Federal Oil and Gas Stripper Well Preservation Act of 1998 - Directs the Secretary of the Interior to provide permanent regulatory authority to make royalty rate reductions for stripper well properties on Federal lands.

Instructs the Secretary to suspend the minimum royalty and per acre lease rental during the period of any royalty rate reduction for such properties for so long as the royalty rate reduction is in effect.

States that, once a royalty rate reduction for such a property is terminated, the lease rental and minimum royalty shall be reinstated to the applicable rate or rates that would pertain without regard to any elapsed period of time during which the reduction or suspension was in effect.