The main issue with this question is the 'One China' policy that both sides have adopted - you are only allowed to recognise one regime as the rightful government of all mainland China and Taiwan, and that must be either the PRC or the ROC (and this also precludes support for Tibetan independence). The vast majority of states opt to recognise the PRC, though the vast majority also have more informal relations with the ROC as well.
Unlike other seemingly similar issues such as Israel-Palestine or Kosovo-Serbia, there's increasingly less motivation to 'solve' the China issue as both sides largely accept the status quo: the PRC accept that without the explicit approval of the Taiwanese population (which is unlikely), Taiwan cannot be annexed; the ROC accept that they're never going to 'retake' the mainland, yet both governments maintain the position that that's what they aim for.
Some in Taiwan want to abandon the idea of the ROC and instead simply push the identity of an independent Taiwanese state, but this is problematic for two reasons:
1. The PRC (and probably Russia too, but that's less important) will certainly block any recognition of an independent Taiwan by the UN.
2. Many on the right in Taiwan don't see much to gain from it; they see themselves as victims of a historic injustice that forced them to flee their homes; rather than Taiwanese, they consider themselves to be exiles from the mainland, and that relinquishing the claim of the ROC to all China would be legitimising that injustice, and all just for a seat at the UN.
As the Chinese Civil War moves more and more out of memory, I expect reason 2 to increasingly disappear, but reason 1 means that the China situation is unlikely to change for some time.