It's not that simple a binary choice.
I'd encourage Steve although (and this is a personal choice, everyone is free to do what they want) I don't know what value, if any, posting "Go Steve" on a thread on an Internet forum actually has. He certainly doesn't read every single thread, if any, and if he does he's (a) possibly wasting valuable time, and (b) going to encounter plenty of negative comments that won't help him. More than likely the gist of things [only the postive stuff if they have any sense] is reported back to him by his team who are reading this and I doubt this includes a list of people who've said "Go Steve" on each thread.
But, despite rooting for him, I don't think he's got much chance at all of beating the record this time round (I'll be more than happy to be proven wrong), but I don't think he should stop yet. My logic goes something like this:-
If he's not going to restart again in the future then me may as well carry on. I'm not sure what my criteria for pulling the plug would be but obviously it's somewhere between the 219 miles per day required (as it is roughly now and I think he should continue) and 300 miles per day (which he obviously couldn't do), but exactly where I don't know. My guess is it's a bit more complicated than that and will be based on whether his start times get later and later, or his average speed starts to drop, or the stopped time during the rides start to get longer and longer, all of which point to the cumulative fatigue becoming too much.
If he's going to restart again then the most obvious date for a restart (in my mind at least) is 1st Jan 2017 to keep the 'calendar year' purists happy and is more in the spirit of the original Year challenge, this also gives himself time to wind down, rest, recover, replan, test new things, and train properly even if he finishes the current attempt on 6th August 2016 I think ~145 days is enough time to do this before he goes again.
Whether or not he has the head/legs for another 7 months of riding, 5 months of some relief (but still some reasonable hard work to give him self the best shot of a new record) and then another full 12 months on is something that only Steve can answer. There's also the question of funding for those 24 months, especially if the replan includes things that cost more (a 24/7 aide, an RV or just lifts to the start of a tailwind) but despite FB's reports on funds we're pretty much in the dark as to what the finances are like (and predicting the future is nigh on impossible).