The question implies some conditions that are not true and border on the illegal. First, the contractor HAS NO RDTE funds. The contractor may be on a contract that is being paid for with RDTE funds, but the funds belong to the government agency that is administering the contract. The contractor has tasks that must be fulfilled within the terms of the contract. The terms of the contract will dictate how long the contractor has to complete the tasks. A government Contracting Officer is the only person who is authorized to change the details of a contract which includes extensions to complete tasks within the allotted time. There are exceptions, but normally RDTE contracts may go for more than one year as long as they have caveats of "subject to available funding".
If the contractor has completed all of the tasks on the contract and did not spend all of the money that was obligated to the contract (as in the case of a Cost Plus contract), then the government agency administering the contract is required to close the contract and de-obligate the unused funds on the contract or otherwise modify the contract to include more tasks. Adding tasks for the sole purpose of avoiding having to de-obligate funds is illegal.
The RDTE funds are Incremental funds and are "Available" for 2 fiscal years. While the funds are Available, they can be obligated to contracts. Contract tasks must be completed within the Available period of the funds. RDTE funds were supposed to be requested based on a reasonable expectation of the amount needed in the first year of the two year Availability period. They are given a two year Availability period to cover the kinds of unknown events (e.g., unexpected delays or additional effort to complete tasks already on contract) that are common in development contracts and to cover odd contract start times that do not line up with the beginning of a fiscal year. While it is possible to obligate 2nd year funds to new tasks (through appropriate contract mods), such obligations become riskier to manage because they will expire on the Expire date.