Why would a replacement 3-way light switch cause the other switch to no longer work?
According to the instructions found here, you'll have to replace the other switch with a Retractive Press Switch when using a dimmer.


  Important notes - for two way and multi - way installation
  
  
  Read General Installation Safety Instructions before starting work.
  Any existing 2 Way or Intermediate switches MUST be replaced with Retractive Press Switches.
  Any number of Retractive Press Switches may be installed provided total cable length does not exceed 50m.
  Either 1 Way normally open or 2 Way Retractive Push Switches may be used.
  If 2 Way retractive switches are used, connect to Common (COM) and normally open L1 (1 WAY) terminals as shown. Do NOT use the L2
  (2 WAY) terminal.
  If replacing an existing 2 Way switch,cut back and insulate the unused 2 way wire previously connected to the L2 (2 way) terminal.
  All Metal Wall Boxes and Metal Plate Switches must be earthed.
  Do NOT connect more than 1 Dimmer in the same circuit,
  Remove label covering centre terminal on rear of dimmer. This terminal is to be connected to Retractive Switch as shown in wiring
  diagram. Do NOT connect any other conductor to this terminal. 
  


However, there does not appear to be a requirement to replace the regular 3-way switch if a dimmer is not being used.  

You might want to telephone the manufacturer to confirm this.

Here is a wiring diagram provided from the above link for non-dimming multiple switches