Chrome browser closed after receving a call I started an online transaction on Chrome (under Jelly Bean). In between, I had a phone call and the browser closed automatically. It disconnected from the web sites, and I had to start the transaction again.

Is there any way to keep Chrome running in background and keep all the connections open?

This is really a big problem for now. I fear starting any online transactions on my Jelly Bean device.

Is there any other browser which will keep the connections open?

Google must have come across this issue.
This is probably because of the amount of RAM on the device you are using. It sounds like the system gave the RAM that was being used by Chrome to the phone app. It saw that Chrome was no longer the active app and the phone app was requesting more RAM so in order to free up the RAM it had to close Chrome.

If Chrome was using a majority of the system RAM, and a new app requested access to the RAM, the system needed to free some up. 

Since you did not specify what device you have though, this is really only a guess.