The petition, which appears to be part of a larger document containing a number of different items, is of uncertain date, and is assigned here impressionistically, on the basis of the hand and the use of Latin in the endorsement, to the first quarter of the fourteenth century. (National Archive note)
I've not found a record of the requested extension being granted.
In June 2003 an archaeological evaluation was undertaken by Channel 4’s 'Time Team at the site of the medieval burgh of Roxburgh, Scottish Borders, centred on grid reference NT 720 340. Time Team’s project design suggested that Roxburgh is the only complete deserted medieval town in Europe.' (Wessex Archaeology, 2004, Roxburgh, Floors Castle Estate
Kelso, Scotland. An Archaeological Evaluation and an Assessment of the results online copy (cf. Caus. Shropshire). The town was defended on the east side by an earthen bank and ditch to which a later stone façade was thought to have been added. The bank and ditch is still visible as an earthwork. The town was burnt in 1207, 1216 and 1243 and its decline accelerated from the late 13th century. It was ceded to Edward III in 1334 and remained in English control until 1460. The date of the town’s abandonment is unknown, but rent records of 1501 suggest an already deserted settlement. (ibid)