My Boeing QRH reads "Above 80 kts and prior to V1, the takeoff should be rejected for any of the following:
* fire or fire warning
* engine failure
* predictive windshear warning
* if the airplane is unsafe or unable to fly
This is an excellent question, and reinforces the fact that you need to be aware and vigilant especially close to V1. The question has two parts for me. Part one the meaning of V1. Is V1 a gate up to which you should have recognised or acted ? I take the view that it is an "action" speed whereby I should have acted. I'm no technical whiz but we are aware that the V1 speed takes into account the fact that an event may have occured just prior to V1 and you have the opportunity to conduct a RTO with said safety parameters intact(refer previous posts).
Part two of the question is really about noises, flight control and recognition of non-normals. I try to simplify the issue by suggesting that firstly we may hear a bang. Next we look at the engine instruments and see if they are "normal". If there are 2 parameters that are not normal then I would consider we may have had an engine problem. Engine failure as opposed to engine damage typically results in continued N1 and N2 rotation.
If the engine instruments appear normal I would certainly consider the possibility of tire damage. We do not have the luxury of EICAS on the 737NG. There are numerous studies on this issue however many have suggested that it would be safer to continue than reject when the aircraft is very close to V1. There are many variables here including runway length, surface condition, wind, aircraft weight etc etc.