Before you dismiss the issue being your PC, you should at least post the PC's specs and what graphic/game settings you are using.

ShB A-Rank CW trains can easily exceed a powerful computer if the hardware, drivers, or game setting are beyond what having 150+ players in one spot can be rendered/handled by the PC.
If you have trouble keeping the A-Rank mark targeted, as in it keeps fading from view, then your system is attempting to display more things that it actually can, and the A-Rank keeps getting pushed further down the in the priority list.
To counter, you need to create a situation of less things being displayed, so the A-Rank mark stays visible.

A few things can help with A-Rank Hunt Trains:
Dismiss your Chocobo and/or Minion, request others do the same.
Fight as close to the mark as possible, use a job that can generate a lot of enmity, and maintain it even if you loose target (Tank stance, Healer AOE heals, DoT skills, No-Target AOE skill, and such)
Reduce the spell/skill effects setting to turn off displaying it from others or others outside your party.
Disable Player Name Plates and lower to minimum Character and Object Quantity.