He does not offer the prayers on time because of his work; should she accept him as a husband?

Praise be to Allah.

Firstly: 

The one who does not pray at all is a kaafir according to the correct scholarly opinion. See question no. 5208. 

As for the one who prays sometimes and not at other times, some of the scholars are of the view that he is also a kaafir. This view was narrated from a number of the Sahaabah, and fatwas to this effect have been issued by the Standing Committee for Issuing Fatwas, foremost among whom was Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him). 

Others are of the view that he is not to be regarded as a kaafir unless he does not pray at all; these scholars include Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) and Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him). 

See question no. 52923 and 83165

Work is not an excuse for delaying prayer until the time for it has ended, because prayer only takes a few minutes. 

If the one who wants to propose to you delays some of the prayers, we do not advise you to marry him, because he is a kaafir according to some of the scholars, and he is an evildoer who is committing a grave major sin according to others. 

Allah, may He be exalted, says (interpretation of the meaning):

“Then, there has succeeded them a posterity who have given up As-Salat (the prayers) (i.e. made their Salat (prayers) to be lost, either by not offering them or by not offering them perfectly or by not offering them in their proper fixed times, etc.) and have followed lusts. So they will be thrown in Hell”

[Maryam 19:50].

Ibn Mas‘ood (may Allah be pleased with him) said concerning al-ghayy (translated above as “Hell”): It is a valley in Hell, very deep and with a foul taste.

If he announces that he has repented and has resolved to offer the prayers on time, and you think that he is righteous in other aspects, then there is nothing wrong with marrying him. 

And Allah knows best.