As significant falls on the lower section of the path are rare I’d not be surprised that the path will remain closed until the cliff above the path has been checked for further unstable rock.
Look out for rockmen dangling over from the cliff top barring away loose chalk.
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Normally the major danger walking on the path is during the seagull nesting season, particularly when chicks are in the nests - I’ve several times been hit around the head by wings or feet of irate seagulls,