Of course the best answer to the thread title
The historical problems have been where the engines are out of the restart envelop and have already spooled down. (due to extremely high pilot workload sorting out what happened).
Recovering from this has more often resulted in hung/hot starts and thermal damage to the turbine rendering any further restart hopeless.
Not a critism of the crew but just food for thought in advance
Also give a thought that if you are at high altitude (volcanic ash etc.) that the recognition of a sucesseful restart will be different than on the ground. The engines RPM and EGT will increase very slowly. While Overtemp EGT is a reliable indication of lack of sucess