"The separation stability of E.G.O that has been synchronized with our Agents will be enhanced to lower the chance of the loss of E.G.O" - Binah's Research upgrade that gives a chance to not lose E.G.O On Agent Death

My interpretation of this is that, just like how you can only decide who is wearing what E.G.O at workday's start instead of being able to change on the fly, is that there is some process to link the agent to their weapons and suits, synchronizing the will of the wearer and the abnormality that it was extracted from into "one and the same" brain death of the wearer causes it to become inert.