Can the candidate keep going on, or will there be a lot of bad blood between the 2 candidates? Trump seems to be toying with this idea, but does he have the guts to do it? I don't think so, but this election has been a ripper, and something diff. always happens. Feedback, good and bad, welcome!
Formally, it is not the candidates who decide who has won. The electoral process continues the same way whatever they say about the issue, with only the courts of each State being available to inquiry about allegations of fraud (if there is some kind of evidence about it). The scenario would not be much different from the 2000 elections at Florida.
The issue of not accepting defeat is that the elected representative of a lot of people will be claiming that the elected president is not the legitimate president, and people from all kind of situations may try to use that as a way to justify their actions, whatever they are... from tax fraud, to disobeying military orders, to outright terrorism1 because the government authority is claimed to be illegitimate.
Imagine what some idiots tried to pull out on the basis of the "birthers" claims or the "sovereign citizens" ideas and increase that by several orders of magnitude. The most extreme2 outcome is that argument permeating into the military and being the base for a coup d'état.
And of course, it sets a very dangerous precedent... from then on, any losing candidate may use the "fraud" card ("it is not my fault because I was a bad candidate, it is the 'black hand'") and the situation may repeat itself again and again.
Note that I am not claiming that these fraud charges could cause a big portion of the American public (or even Trump supporters) to do stupid/illegal things, most of them will just ignore Trump claims unless he can provide some actual evidence. The problem is that even if these allegations only motivate a 1% of Trump supporters, it would be still a number of people large enough that could cause serious trouble.
1 You know, you cannot honestly be constantly repeating things about "the blood of tyrants" and that you are going to jail political opponents and claim that the elections are rigged and then be surprised if some people interpret this as a signal to start killing the "tyrants" and their "henchmen".
2 Despite all, this possibility is very, very, very, very unlikely nowadays in the USA, but it has happenned in other countries.