I was playing a blitz with java client 3.5.11.

I had 4 ou 5 periods of byo-yomi left, and I was waiting for my opponent's move. I saw his countdown going to 0 and I thought I had won by time, but there was no message announcing my victory, as if there was no connection to the internet.
Then 3 seconds later, I got a message telling that I had lost by time. My opponent was credited again with 5 byo-yomi periods. I didn't get a chance to see my opponent's move and play.

It seems to me that in such a case the client could detect that there was a problem and start my countdown when it received the move, doesnt'it ?

Probably a disconnect from the server. The client tried re-calling to the server, eventually did but by then the game was over. The opponent time gets counted by your own client, and synced after the opponent moves. So the fact that you saw his countdown finish does not mean it actually did.

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This sounds like a case of net lag. Unfortunately, just about the only thing you can do of you suspect you are lagging in a tight time situation is close your client and relogin. If kgs never receives a response from you, it will not time you out, so it may save some or all of your clock by doing this. Otherwise, once kgs gets that response from you it will sync the clock and all the time elapsed is counted against you.

Handling clocks client side is a risky option because it opens the door to time cheating.