Is it possible to be reborn for all eternity?
Many people are interested in living forever (eg Christians) because such people do not think living is suffering. Instead, they wish to spend forever with their loved ones. That is why they are not queuing up to practise Buddhism. 

My impression is Buddhists are similar, in that they wish to believe in reincarnation so they can live more lives. That is why most Buddhists are not practising the path, hardcore, but preaching that Buddhists must believe in reincarnation, rebirth, whatever. 

Also, Buddhism does not state making merit ends suffering (SN 12.51) so what is its relevance?

Also, Buddhism does not state all beings are destined for enlightenment (AN 10.95).

Imo, the questions are an extreme &amp; pointless misrepresentation of Buddhism. If the questioner truly believe they were suffering, they would be a monk urgently putting out the suffering, like as if their hair was on fire.