Remember that the pykrete experiments didn't end very well.  If one was building something as large as the Titanic, I would assume there would be a need for a more permanent material.  However, perhaps these pykrete experiments will lead to a new, futuristic building material that draws on the flexibility and other natural features of pykrete.  

You could also look at the modern cruise ships.  How do these vehicles detect ice bergs and other dangers?  I would certainly want to include a fair amount of modern technology in my design.  Technology such as radar, sonar, GPS, etc.  Even a simple GPS unit would have allowed another boat to radio the location of the ice berg to the Titanic.  While cruise ships do still have accidents today, it is far less catastrophic than the Titanic.

If the pykrete was used on a massive scale, like say Titanic-sized, the rate of melting would be so minimal that it would not be a big deal.  Post #8 had a good idea about two hulls, and the Titanic could routinely chart its course through colder, northern areas to help with refreezing.

I think that pykrete (which is a really interesting idea!!!) would indeed slowly melt away over time - however you could embed refrigerating coils inside it to keep it chilled. It would take some energy, but it should work.

A more mundane solution is to use a double hull, a technology which is common on modern ships. This consist of two hulls one inside the other. Perhaps you might want to think about making the outer hull of pykrete and an inner hull of another substance.

The first thing I thought of is the new technology in cars which not only sees objects the driver can't see but also stops the vehicle whether the driver hits the brakes or not. Put this on all sides of the Titanic and perhaps the accident never happens, though stopping a car is certainly easier than stopping a giant ship. 

Are you allowed to be futuristic?  I mean, can you give it radar so that it could more easily detect icebergs?

Outside of that, what about a huge airbag?  When the ship hits something hard enough, the airbag deploys.  That acts as a flotation device to keep the ship up while it can be evacuated.

A really creative, out of the box, idea would be to fashion your Titanic out of pykrete--a combination of sawdust and ice.  There was actually a top-secret project in World War II to build air craft carriers out of these, because ice floats--the ships would be unsinkable!  The frozen ice and sawdust material is also incredibly tough and durable. 

The Mythbustersshow recently featured this idea, and took it one step further by using frozen newspapers. 

If the Titanic had been made out of pykrete, it would undoubtedly have remained afloat, because of the composition of the building materials.