When I apply the brakes, the pedal goes about half way down ---if I pump them one time they are at the top and very strong.... I have bled the brakes the "old way" having a partner push the pedal, etc., and also have had them power bled.. Same problem..
The pedal does not sink to the floor when you keep it applied for a long time(used to be the test for a leaky master cylinder...).
All of the pads and rotors, and all of the calipers are in really good shape with no visible leaks---hoses and connections as well...

Any suggestions???

 

Sounds like you are about to buy a new master cylinder. Rovers have always had a firmer pedal on the second hit but it sounds like yours is about to fail.
What brake fluid have you been using?

 

Since I just got the Rover a few weeks back, I don't know----when I did the bleed, I used Prestone Dot 4 which carries the JMV designation...

After I bled them, I see BA recommends the Castrol GTLMA....

 

You dont have to use the Castrol LMA brake fluid, thats what it came with, but you dont have to use it.
(Castrol is a British company so they want you to use British stuff, makes sense)

 

Prestone is really the only Dot 4 fluid I can find locally so that is what I use also.