Cold the Trump grows, but stubbornly uncommunicative. In Gawain's experience, this means one of several possible things.
First, the person portrayed by the Trump might be dead. Trumps of dead people gradually turn into ordinary playing cards, but the process takes centuries. Corwin, last seen as recently as four years ago Amber time, could easily have faced misadventure in the last few years, and his Trump would yet have the psychic chill and other features of Trumps without anything to connect to on the far side.
Second, the person portrayed by the Trump might be out of range. Under ordinary circumstances, Trumps can not reach across the entire breadth of Shadow from any given point in it. Someone out of range of a Trump call might not even notice they are being called.
Third, the person portrayed by the Trump might be somehow blocking the call. This can be done simply by emptying one's mind of all thoughts, concentrating on nothingness, or it can be done via a variety of mystical means — certain locations are difficult or impossible to Trump to, spells and wards can block Trumps, etc.
Fourth, the person portrayed by the Trump might be engaged in a Trump call to another person already. Gawain has heard rumors that some people might be able to simultaneously engage in two Trump connections, but has never seen evidence of it with his own eyes, and has no reason to suspect that Corwin is particularly capable of manipulating the rules of Trump.
In any event, after thirty minutes of deep concentration, not the faintest hint of thought or response issues forth from the picture of the man in black and silver.
IMC, these rules would be general experience as well—though the 'dead' royal rule does not apply.
IMC, Psyche has been known to overcome wards or spells. The trickiest one of the above to guess or overcome is the 'certain locations' block.
Psyche determines effort to cross distance with Trump. Endurance determines unusual Trump stunts, such as bringing more than one person through a connection, or moving a body of troops through a Trump, or charging a Trump gate to open for a time. These are combined feats of concentration (psyche) and strain (endurance.)
And very important is sending time, which IMC might be five minutes for an experienced Trump artist and forty minutes for a weaker psyche with no Trump talent. Distance determines how long before a connection can be made. A Trump call from Chaos to Amber is usually impossible.
Place Trumps are always weaker than person Trumps and more likely to fail.