In discussing the role that the Trinity played in our election (selection, salvation, justification, redemption), it is important that we define terms. We are elect: it is a present state of being. But God’s election of us is not arbitrary, it is based on our faith, born of free will (cf. John 3:16-18, Romans 4:23-25). A good way to put it is this, “God chooses us when we choose Him” (and God gives all people a fair choice according to His foreknowledge).
Despite the baggage the word has come to acquire, elect simply means that we are presently selected by God to be part of His family through our non-meritorious faith in His Son and His sacrifice. Thus, the phrase “the elect” is synonymous with “all believers” — by definition, all believers are elect, because God selects every believer into His family at the point of their salvation (that is, after all, what salvation really means). What “the elect” does most assuredly not mean in scripture is a group of people that God has arbitrarily chosen to be saved no matter what they think about Christ or what they do with their free will.
The statement that none of God’s elect are lost is true because the elect are believers and no believers are lost. The statement that all people presently elect will be elect tomorrow by virtue of being elect today does not follow from the above, so long as one understands that being believers (and hence elect) is something we choose daily. Our status before God is conditional on our faith in Christ. With such faith, we are washed clean in His blood, made Holy before God, and adopted as sons and daughters. Without such faith, however, we have no basis of justification before God, we lack the righteousness of Christ imputed to us through belief, and we will be eternally separated from God due to our sin. Previous faith does not guarantee present election; present faith does guarantee present election; preserving present faith is the only way to guarantee future (and eternal) election.
If one wishes to call the group of people that God (and not man) has foreknown as saved in eternity (i.e., the group of believers that will maintain their faith until the end) “the elect,” then one needs to be careful to distinguish this group from the definition above in some contextual way. The two groups are different, and it is the conflation of these groups that has caused so much confusion over the years. My personal opinion is that we should use “the elect” as a phrase to describe the body of believers currently selected by God on the basis of their present faith in Jesus Christ (as scripture does), and “the eternally elect” as a phrase to describe the group that God has foreknown as being eternally saved due to their perseverance in the faith. There is always significant overlap between these groups, but that does not make them the same.