Raspberry Shoots that Die or look unhealthy, could be suffering from the maggot - caterpillar - of the raspberry Moth.
Inside the stem of the Raspberry cane - feeding on the pith, if you find a red maggot larva around 1cm long, then it is probably the larva of the Raspberry Moth. It lives overwinter in the soil, then emerges in March April to bore its way into the stem of the canes and then eats the lifeblood of the cane - the pith - and results in the Raspberry cane dying back.
Winter tar wash has some effect, and should also be sprayed on the soil around the raspberry canes.
If the caterpillars are seen, then a contact insecticide containing Bifenthrin can be used.
The raspberry moth is brown in colour with a wing span of around 12cms. rapid beating of the wings - typical of moths.
Cut off and burn withered and dead shoots - canes.