Constant reload of CH34xx driver

Are you using a Pro Mini, or is the 'Mini-Pro' that you're using a different thing altogether? If it is something other than a Pro Mini, can you post a link to it?

Steve-SFX:
OK. Bought another 3.3v 8Hmz Mini-Pro + USBasp programmer lead from Bitsbox.
Nope... still totally ignores it.
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When you use an external programmer like a USBASP, you need to select the correct programmer via 'Tools>Programmer', and then use 'Sketch>Upload using Programmer'.

Steve-SFX:
I just cannot get any of my CH34xx Mini Pro's to program any more.
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Doing what I usually do - use an UNO to program them with. TX-TX, RX-RX, 5V to 5V and ground to ground.
Reset to reset doesn't seem to work, not does playing around with the DTR pin on the Mini pro.
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Yet, I can appear to write the code to the UNO.

If you can upload code to the Uno then the USB-Serial side of things is working. It is more likely there is a problem with how the Pro Mini is connected. Can you post a photo/schematic?