Deals die 2-3 times before they close. This is never easy to accept and when it is happening it is stressful. The moments I have found when a deal is most likely to die are:
Signing of the LOI. A well-thought-out LOI should have a good portion of the terms of the deal included. Pressure points will come up and a middle ground will have to be found. This is an opportunity to find consensus and come together. This will begin to build trust for the rest of the transaction.
During the Due Diligence. The due diligence process is extremely stressful for the seller. It is a ton of work. Sometimes they take it on themselves personally due to a fear of people in the company learning the business is for sale. This is a mistake. They need help getting the information for DD. Be patient, be understanding, and help them through it.
Near the close. Stress levels increase, you are missing some final approval from a vendor, or an issue occurred in DD that needs to be resolved. By now, if you built consensus and were helpful in the process, some trust should have been built. You and the seller are sitting closer to the same side of the table, instead of on opposites. You both have a common goal, the culmination of the transaction.
The buying of a business is a process. Building trust throughout that process is the best way to overcome the inevitable difficulties that will arise.