IIRC, Col. Gracie contacted a majority of the survivors for his book, "The Truth about the Titanic" (and reprinted as "Titanic: First Accounts" in the 21st century). Its a brilliant book with a lot of primary sources from the survivors themselves.
The best example of this post-disaster long term communication was between Lucy, Countess of Rothes and Able Seaman Thomas Jones, both of whom were rescued on Lifeboat #8. As is well known, the Countess manned the boat's tiller for a while and at some stage also helped to row. In recognition of that work and helping in soothing other distraught passengers on the boat, Jones presented Lucy with a brass plaque showing the number of Lifeboat #8; she in return later gave him an inscribed silver watch. The two then exchanged letters and Christmas Greetings, the latter supposedly till the Countess passed away in 1956. Jones outlived his unlikely pen-friend by 11 years.