Hebrews 10 says Christians are to stir one another up to good deeds, “not forsaking our own assembling together” (v. 25). But, what does that mean? The key term “forsaking” translates the GK word egkataleipontes (pres act ptc nom pl masc), which is from the lexical root egkataleipo. According to Mounce, the term is rightly glossed to read “to leave, to leave behind, to forsake, and abandon.” BDAG says it means “to separate connection with someone or something., forsake, abandon, desert.” Kohlenberger adds “to give up.”
The writer to the Hebrews uses the word only one other time. Hebrews 13:5 says, “God has said, Never will I leave you; never will I forsake you.” The word “leave” does not have the same finality as “forsake.” The idea of “forsaking” carries the notion of total abandonment. Paul uses the term in 2 Tim 4:10 and 4:16 to speak of those who totally abandoned him. “For Demas, in love with this present world, has deserted me and gone to Thessalonica” (2 Tim 4:10). “At my first defense, no one came to stand by me, but all deserted me” (2 Tim 4:16). Therefore, the GK term translated "forsake" in Hebrews 10:25 means that the believer must not abandon the Christian assembly.
In conclusion, this text does not mean that a person must come to the assembly every time the doors are open. Rather, it means that we must not “abandon” the assembly. But, what does that mean? Is the notion of abandonment purely subjective? If people come regularly for Christmas and Easter every year, have they “abandoned” the assembly? What if they come once a month and never more, but they come consistently every month? How do we know when someone has abandoned the assembly? Is it purely subjective? I submit that unless we have a clear doctrine of the Sabbath, then we have no objective measure by which to decide what “forsake” means. I would argue that to “forsake” the assembly means unrepentantly breaking the Sabbath (which includes exceptions for acts of mercy, piety, and necessity: Matt 12).