Aaaaaaand I answered my own question by digging a bit deeper into your forums. I found this thread: http://support.advancedcustomfields.com/forums/topic/repeater-field-values-disappearing/
And discovered that dropping the following into my htaccess file fixed it:
php_value max_input_nesting_level 128
php_value max_input_time 300
php_value max_input_vars 3000
php_value max_execution_time 300
php_value post_max_size 32M
Though I haven’t tested on my live server, only localhost, but I think that my problem was the max_input_vars thing. Yay!
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