Buy some "rubber renew". The pinch rollers that move tape depend fundamentally on having some traction to do so. And what can happen over time is that they get hard and smooth fro all that rubbing. Yu need to make them rubbery again. I'm not saying that will necessarily cure the beast, but the reason these rubber-renewal products exist is BECAUSE that has been an eternal problem with tape-based technology.
This may not be the certified best product on the market, but it was the first one that came up in my browser and is readily available at many industrial electronics outlets.