This would’ve been a conundrum if God has obligated on us to pray on specified time at all costs, irrespective of the circumstances or difficulty we are going through. For all Ibadah (Prayers, Fasting etc.), the principle has been laid down as such.
Take prayer (salah) for example:
i) In normal circumstances, all effort must be made to perform that prayer within the framework of the rules (time, procedure etc.) laid down by the Religion.
ii) In case of any hardship (mushaqat, Usr), the same prayer can be performed in its closest secondary form & two prayers can be combined or even reduced to half depending upon the hardship, for example, if it’s difficult to stand up, one can pray on a specified time while sitting down or in worst case scenario, via hand signs only.
iii) If due to any circumstances (social/contractual obligations for example), you cannot by any chance excuse yourself for prayer, you can pray whenever your situation gets back to normal where you can spare time for prayer.
In the presence of all these relaxations, it is practically impossible for prayer (salah) to create any form of hindrance in performance of your obligatory social/contractual duties and responsibilities.
If one has truly recognized God and established a relationship with Him, it is hard to believe that one will not try his level best to connect with God and remember Him in the given circumstances. Still, after all his tries, he is facing impediment to do so, he can avail any of the options above. Thus, there is no room for any conundrum to exist.