Is there a set limit on the time between tawaaf and saa’i?

There is no set limit on the time between tawaaf and saa’i. Doing one straight after the other is not an essential condition, but undoubtedly it is better for a person, once he has done tawaaf, to do saa’i. The Prophet (blessings and peace of Allah be upon him) did his saa’i straight after doing his tawaaf. But if a person delays it and does tawaaf at the beginning of the day and saa’i at the end, or one or two days later, there is nothing wrong with that, because doing saa’i straight after tawaaf is not obligatory. End quote. 

Majmoo’ Fataawa Ibn ‘Uthaymeen, 22/421