The answer likely depends on the exact terms of your (previous) lease, so you need to take a careful look at it. The experienced mineral owners will always include an "Exhibit A" (appended to and incorporated into the lease), which modifies the terms of the standard lease to make it more equitable for the mineral owner. One of the (several) clauses in such an Exhibit A will likely be a DEPTH CLAUSE worded somewhat like mine, below.
DEPTH CLAUSE: Notwithstanding anything to the contrary in said Oil and Gas Lease, at the end of the primary term of this Lease, this Lease shall expire as to all formations, horizons or zones that lie below 100 feet below the stratigraphic equivalent of the base of the deepest formation found to be capable of producing in any test well on the lands herein described or lands being part of the same drilling and spacing unit therewith. However, if Lessee is engaged in operations which would otherwise extend the term of this Lease, the Lessee has the right to complete said operations before this provision is effective, and such operations shall be considered to have been completed prior to the end of said primary term.
If you have a clause like this in the original lease, then you're likely completely free to lease again (below the indicated depth) and receive lease bonuses.
Please note also that if the property is, indeed, held by production, that doesn't just free the new lessee from paying bonuses, it invalidates the new lease, so don't let them claim that you're bound by the new lease but they're not bound to pay the bonus. In this event, only the terms of the old lease apply. Hope it was well negotiated.