When reactants are in their transition state, can they go back into their reactants form instead of progressing to form the products?
In the gas phase the reactants have kinetic energy as they move towards one another, so you would think that they would just cross the transition state, but molecules also have vibrational energy which means that it is possible to reach the transition state and then turn back. See the figure below which shows a simple LEPS calculation of the O+H2 reaction. 

The solid black line shows the position and vibration of the H2 molecule as it approached the O atom and then 'reflects' at the transition state. It has just enough energy to cross, but the vibrational motion and position on the energy surface prevents it.  The axes show the separation of H and H2 (mid point) and of H and OH products.



In solution (or high pressure gas phase) the situation is a little different because collisions with may solvent inhibit or enhance the motion of the reactants towards one another. The species diffuse together and also diffuse along the transition state pathway so that the transition state can be crossed and recrossed many times before reaction occurs or the reactants are reformed. This approach is named after Kramers and is the most important one to understand when thinking about transition states in solution. (Strangely, it is rarely mentioned in Chemistry textbooks even though it was developed more than 70 years ago.)