I had one deal where this was needed, several years ago.  I went to the agent's Broker instead.  The second time I had to go to the Broker, we told him if it happened again we would need the agent replaced.

I would not contact another agent's client directly. But I would contact my broker-in-charge who would contact the other agent's broker. Had to do that just last month, in fact. Fortunately, not something I've had to do many times.

I've had the buyer call me because their agent was MIA & they were scared. Called the agents broker for them. 

You always had to tread lightly with this & it differs in each state.

I would first email, text the other agent then reach out to their brokers before reaching out to the people involve in the deal!

I have done it, Richie.   

   I recall a missing Broker on my listing; she had the Buyer.  The home inspection appointment was approaching, no confirmation.  And no word from the Lender, nothing but silence.  

    I documented my numerous unsuccessful attempts to contact her (in case of COE complaint, or tortious interference).  Then I asked the Title Attorney to call her for further "proof" that she was incommunicado. 

    I called the Buyer, who was also puzzled "Where is my agent?".

    The missing Broker finally showed up.  I think she had been on a binge or had some sort of nervous breakdown; I didn't pry.  We closed the deal.

I believe there is a time when taking such action might be necessary.

Contacting the broker is a good recourse as well unless the agent happens to be the broker in which case - direct to the client. 

There are some agents who do not want their client talking to the other agent.  I am not in that camp.  If I couldn't get a hold of the agent, I would call the broker.  If I couldn't get the broker, I would call the other client and ask them if they are trying to sell the house.

I have never had to do that.  But some agents are more of a hindrance than a help.

Also, some agents have a different goal in mind.  I had a listing agent say to me a few months ago, "This has only been on the market for 30 days..."  I said, "Are you trying to keep it on the market for as long as possible?  Or is your goal to get it off the market?  My goal is to get it off the market."  I wouldn't have any problem bypassing an agent like this.

We should start with the brokers, first report to yours and then go to the other agent's broker for permission to approach the other agent's client or to get responses. 

Our state has rules in place about this.  We have to document attempts to make appointment, present an offer, then contact broker, then if still no response we are allowed to contact.  But it's never had to happen in my 9 years.

straight to the agent's broker. A manager, with their license on the line, will cooperate. If not you can take the Professional Standards route but your customer can file a complaint with the state licensing commission. Not a good thing.

I shift this type of activity to my Broker and let them deal with it Broker to Broker. The result is painless and much faster that way, usually within 24 hours or less.

Interesting . . . my office's attorney recently posted to FB the Commissioner's list of recent and most plentiful complaints. One was 'can't reach the agent'.

In AZ it has always been "24 hours and go to the broker; 24 hours and go to the seller" . . . if you are not getting responses.

I had an agent ignore my (material) question for days, and he was CCing the seller in communication with escrow (dumb). So I posed the question to seller CC everyone . . . got a nasty from the agent for 'talking to his client' and then I CCd the broker and told her school her children! The agent tried to make an excuse that 'he was on a plane' REALLY dude? For 3 DAYS STRAIGHT? Save it. He likes me now. LOL

As buyer's brokers the LAST person we want to deal with is the seller! Seriously. But agents that put their clients with the other agent deserve what they get. 

I recently was alone with a seller, contractor in tow assessing the cost of repairs. She told me 'If you ask for anything, I'll move on. I gave you X discount already' okay babydoll you opened the door, "Of all the homes in your area that sold past 6 months, ALL but one was 190 PSF or below. You were at 206. We gave you 200 which was generous."

I waited for the listing agent to carp at me . . . she did not.

We got the repairs. 

We list it, market it, sell it (Repeat). Small rural markets don't have the layers of players or delay in communication.

No, sometimes you can contact their broker, most of the time we just move onto another property, or wait for this one to expire.

I would not advise speaking with another agent's client unless they contacted me.  Even then, I'd never cross the line of agency.

I would not contact the agent but rather the agents broker.

As several have mentioned, I would work through my broker to the other agent's broker before trying to contact the client directly. I would pursues a quick and permanent resolution so my client could move forward.