Martha Jones never had a chance. Her pining after The Doctor got stale pretty fast because that's all she got to do, which is a shame, really.
It wasn't difficult to identify with Rose Tyler because I got to know two "new" Doctors through her eyes. He changed, and she changed a little because she stayed with him.
With Martha, that didn't quite work because I already knew more about The Doctor then she did, so I identified with The Doctor rather than with her.
I hope the new companion will be someone who's not from this time and/or planet. Such a character might offer a fresh perspective on our world and might be interesting to get to know. Simply replacing Martha with some other potential love interest for The Doctor wouldn't be a good basis for a compelling character, IMHO.
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It wasn't difficult to identify with Rose Tyler because I got to know two "new" Doctors through her eyes. He changed, and she changed a little because she stayed with him.
With Martha, that didn't quite work because I already knew more about The Doctor then she did, so I identified with The Doctor rather than with her.
I hope the new companion will be someone who's not from this time and/or planet. Such a character might offer a fresh perspective on our world and might be interesting to get to know. Simply replacing Martha with some other potential love interest for The Doctor wouldn't be a good basis for a compelling character, IMHO.