Depends on which convulvulus you're talking about, which one is it?

Not sure, white flowers maybe they all have! I only planted them last year but I think the frost got them as most of the leaves are brownish. Thanks for replying. Ann

If you mean Convulvulus cneorum (white flowers in April or May, grey leaves, evergreen) trim over after flowering. Mine have lots of browning on the leaves too, though the new growth is as it should be.