"It is a sign forever" — the Mekhilta derives from this phrase that the Sabbath will never be lost from Israel. No matter what happens — exile, persecution, assimilation pressures — the Sabbath will endure.
The Mekhilta then establishes a striking principle. All the things that Israel gave their lives for have endured permanently: the Sabbath, circumcision, Torah study, and ritual immersion. These four practices survived every catastrophe because Jews were willing to die rather than abandon them. Their willingness to sacrifice guaranteed their perpetuity.
By contrast, all the things that Israel did not give their lives for did not endure: the Temple, the shemitah years, the Jubilee years, and the institution of judges. These were lost when circumstances made them impossible to maintain. No one died to preserve them, and they did not survive.
The correlation is exact. Willingness to die for a practice equals permanence. Unwillingness to die equals impermanence. The Mekhilta is not praising martyrdom for its own sake. It is making an observation about the relationship between sacrifice and survival. The practices that form the core of Jewish identity — the ones Jews refused to surrender under any circumstances — are the ones that have lasted thousands of years. The Sabbath is "a sign forever" because Israel has always been willing to make it so, at the cost of their lives.