On the particular subject of suicide, I cannot comment other than to recognize that in PeaceInChrist case, it seems that God DID ANSWER - it was avoided because someone was there.
On the general subject of ‘unanswered’ prayer more can be said. I will try to present just a few points for consideration.
We should always remember that God answers prayer in His own way and in His own time. Saint Monica prayed for 15 years that her son give up a life of sin and come closer to God. 15 years. Her incessant prayers were more than answered. He not only gave up sin and came closer to God, he became a Bishop and we know him as St Augustine, one of the top 5, if you will, theologians of all time.
We should always remember that if God seems not to be answering our prayer, He is nonetheless WITH US in our struggle, providing us His Grace to carry on. Perhaps there is a greater lesson or good to be achieved because we have to struggle longer than we think proper.
Perhaps we are praying and not doing the other things to make our prayer more meaningful. Are we in the State of Grace? Are we receiving the Sacraments as often as we should? Are we giving Love to others that we are asking God to show us? Do we ignore ideas that come to us that could help answer the prayer?
More can be said and I hope others will say it.