This is from a "Test" section, so I had no hint that it was a mate problem. I am down to 4 minutes per problem, though I didn't even use all my time before I started guessing (bad!). Perhaps I was a little tired, but that's not much of an excuse. After not seeing any way to stop both pawns, I just started making lazy mate threats which FINALLY yielded the quiet answer of Rg56. Tricky, huh?

Qxh7 just posted about this, namely how is it that it's difficult to see mate in 2 when you can see easy mates in 3, 4, or even more. In spite of individual differences, I think players experience a similar phenomenon early in there career. To share my take on the whole issue, I have created some relatively simple forced mate examples, all White to move and all with a weak wrong move(s) possible.

• Outnumbering: when cautious middlegame mentality gets in the way. If I ever get good enough to write a tactics book, outnumbering would be the largest chapter. Here are two positions with this theme that seem essentially equivalent to me, the only difference is the second one is difficult for more people to see right away.
  
  
  
  
  
  
  Same answer for both positions
  Weak move: Rd8+
  Answer: Rxh3+ gxh3 Rxh3#
  
  
  
• Option Limiting: failing to see a quiet move, prophylaxis, or zugzwang. The second example is a test of finding the absolute best moves for both sides.
  
  
  
  Top postion
  Weak move: Rb8+
  Answer: Ra7 any Rb8#
  
  Bottom position
  Taking the Queen is obvious, so after Bxc7
  Weak move: ...Nxc7
  Answer: ...Nd6
  Now after Bxc7 Nd6 we get
  Weak move: Bxd6?? or Nf7? or Kg3?
  Answer: Several moves will work-Kh1, a6, Bb8, etc.
  
  
  
• Uncommon Final Pattern. The TCT at the top certainly seems uncommon to me.
• Uncommon Tactic: destruction, clearance sacrifice, unusual looking absolute pins, multiple Tactics.
  
  
  Weak move: just about anything other than the answer.
  Answer: Rxc6!. Now ...Bxa4 is the only way to avoid b5#, but leads to Qxa4#
  

Remedy

I'm not all that experienced like a trainer, but I can speak to what I do. After I follow the forcing checks and moves and not finding the answer, I attempt a few things which have helped me to shift towards the solution in the past:

• Review it. I still make mistakes calculated, so I can tend to go over it again to see if I have messed anything up.
• Break visual attention/move around (like for 30+ seconds). Actually this one has been more helpful than trying to think tactically.
• Look for any possible absolute pin, no matter how unlikely it looks.
• Break the rules. Calculate if you could move on top of or even through your own pieces, or make two moves to achieve mate. This is known as "null move" thinking, and is a powerful optimization in computer chess engines.
• Finally review the "Fundamental Checkmates" and attempt to apply it to the position.