Task Orders and Extending the Period of Performance

So please excuse my ignorance here, but I have a question. If a task order, under a multiple award IDIQ, expires, is it possible to "resurrect" the order at a later date? Say a month after a task order expires we find out that more work needs to be done at the same location. Can we use the same task order and correspondingly any excess funds from that order, to complete the work or does this require a new order? All this assumes the underlying contract is still active and valid, and that for various reasons competition would not play into this decision.

I've been searching all over the FAR for an explanation of what the end of the period of performance means, but I haven't found one for task orders that really seems to apply. Thanks in advance for the advice.