Can You Take a Break between Tawaf and Sa`i?

Yes, there is nothing wrong with delaying Sa`i after Tawaf , although it is better to do Sa`i straight after Tawaf . 

Ibn Qudamah (may Allah have mercy on him) said in Al-Mughni (10/240): 

“It is not obligatory to do Sa`i immediately after Tawaf . 

Imam Ahmad said: There is nothing wrong with delaying Sa`i until one has rested or until evening. 

`Ata’ and Al-Hasan did not see anything wrong with the one who had circumambulated the Ka`bah at the beginning of the day delaying As-Safa and Al-Marwah until evening. This was done by Al-Qasim and Sa`id ibn Jubayr.” 

It says in Fatawa Al-Lajnah Ad-Da’imah: 

“The Sunnah is that Sa`i should be connected to Tawaf as much as possible, but if one delays Sa`i a great deal and then does it, that is valid. 

And Allah is the Source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions.” (Shaykh `Abd Al-`Aziz ibn Baz, Shaykh `Abd Ar-Razzaq `Afifi, Shaykh `Abdullah ibn Qu`ud. Fatawa Al-Lajnah Ad-Da’imah lil-Buhuth Al-`Ilmiyyah wal-Ifta, 11/263) 

Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: 

“It is not essential that Tawaf and Sa`i be done one after the other, even if there is no reason for that, so if a person does Tawaf at the beginning of the day and Sa`i at the end, there is nothing wrong with that, or if he does Tawaf at the beginning of the night and Sa`i during the day, there is nothing wrong with that, because doing Tawaf and Sa`i one after the other is Sunnah, not obligatory.” (Majmu` Fatawa Ibn `Uthaymin, 23/201)

And Allah knows best.