Answer: The String Breaks!

Station Frame: The distance between the ships is constant. The string length contracts at high speed; the space between the ships does not.

Lead Ship Frame: The distance between the ships is increasing. The lead ship sees the trailing ship slowed down. Why? If the trailing ship sends out light pulses every second, the lead ship will receive them slightly longer than one second apart.

Trailing Ship Frame: The distance between the ships is increasing. The trailing ship sees the lead ship speeded up. Why? If the lead ship sends out light pulses every second, the trailing ship will receive them slightly shorter than one second apart.

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