It sounds like the wood of the block has deteriorated in some way (oils drying out, fungal attack) so that it can't maintain dimensional stability through a wet/dry cycle. Whether the high notes or low notes work better depends on the positioning of thelabium in the air stream - move the stream outwards and the response goes one way, move it inwards and the response goes the other. You want it in the middle. The swelling and shrinking of the block affects that - as the block swells, it pushes the airstream outwards relative to the labium.

Have you taken the block out to clean it? Accumulated dirt and mould might produce the effect you're finding.

If you consider the instrument worth the expense, you could try a trick I use with clarinet and sax reeds. Soak the block in alcohol - I use gin; vodka would be better but I don't drink it. Keep it soaked and only take it out to play it. This will both kill off any fungal and microbial cultures and improve dimensional stability. (With reeds, they last about ten times longer). But it won't be long before you've spent more on your instrument's booze habit than you'd spend on simply buying a new one. We have a thread in BS at the moment that comes to much the same conclusion about supporting alcoholic husbands and wives.