The words "go on increasing in disbelief" refer to being disbelievers until death. This is reported from Ibn Abbas and also Mujahid.
Ibn Kathir says:
Ibn Abi Hatim recorded that his father said that Ahmad b. 'Abdah
related that Hafs b. Jami' said that Samak said that 'Ikrimah reported
that Ibn 'Abbas commented;
ثُمَّ ازْدَادُواْ كُفْراً
(and go on increasing in disbelief), "They remain on disbelief until
they die.'' Mujahid said similarly. (Ibn Kathir 4:137)
Allah says in another verse similarly:
And whoever of you reverts from his religion [to disbelief] and dies while he is a disbeliever - for those, their deeds have become worthless in this world and the Hereafter, and those are the companions of the Fire, they will abide therein eternally. (2:217)
So, the verse is not to be understood as saying those who apostate twice cannot repent. Rather, it means those who died as disbelievers will not receive God's forgiveness.