It’s not any help to you RIGHT NOW, but there was an RFE recently (Request For Enhancement) to cover a “Client Helper” component similar to what is available under Windows but for Linux systems. One of the features of that helper would potentially be to restart a stopped BES Client process.
If you have not done so already, search the Forums to find the thread about it and use the link in there to go “Vote” for the RFE. The more Votes and RFE gets the greater the chance that IBM will devote resources to making it reality.
For Reference: The thread was RFE - Watchdog service for BESClient