If you occasionally have to press in a bass/mid driver to get it working normally, what would that fault be? With the driver itself or somewhere else?
It sounds as if there's damage to the voice-coil causing it to jam instead of moving freely back and forth as it's designed to do. When you press it can you feel any resistance or 'rubbing'?
Any voice-coil that's working properly should move freely back and forth if you gently press the dust cap when there's no signal present, like a well lubricated piston.
You can only be young once, but you can be immature for ever.....
The speakers are asked about are not mine. It seems the driver plays fine once it gets going but just occasionally needs a push to get pumping. From what you said it could do with being replaced.
Just watching a reasonable pair of speakers and have come across an ebay bug bear of mine - the seller wants to pass on his ebay seller fee to the buyer (and, no doubt, his paypal fee if paypal is used) and has quoted over £17.00 just for packaging £50 used speakers. If you reach a potential worldwide audience to sell something, why should the buyer pay the seller fees?