Most phones and many testers are equipped with 6-position modular plugs, but many jacks are 8-position.
When a 6P plug is inserted into a 8P jack, the outside "shoulders" of the 6P plug will push against pins 1 and 8 in the 8P plug, and the two outer pins may be deformed beyond their ability to return to normal position. If this happens, the deformed pin will sometimes cause the jack to have open circuits when an 8P plug is used.
If you find this problem, and know that the jack needs all 8 pins, replace the jack with another 8-pin jack.
If you know that the jack does not require all 8 pins, replace it with a 6-position jack.
(Diagram from ICC)