The main problems faced by the UPC are logical impossibilities relating to EU law.
For example, CJEU opinion 1/09 (http://curia.europa.eu/juris/document/document.jsf?docid=80233&doclang=EN) indicates that any pan-European court, such as the UPC, that supplants the jurisdiction of national courts must be "situated ... within the judicial system of the European Union", for example by being a court common to (only) EU Member States.
On the other hand, the only thesis that has been advanced in support of the UK's post-Brexit participation in the UPC relies upon the assumption that the UPC is an "international court".
It is a logical impossibility for the UPC to be both an international court AND a court situated within the judicial system of the EU. Thus, the UK's participation is clearly precluded.
Another example is the (strong) desire of the UK to ensure that CJEU rulings no longer apply to the UK post-Brexit. Once this ambition is achieved, then it is impossible to see how the UK could participate in a court that is required to make references to, and to follow the rulings of, the CJEU. This is because members of the UPC will be obliged to enforce the judgements of that court ... and to therefore ensure that their national laws can only ever be interpreted in accordance with all (future) CJEU rulings that could possibly have a bearing upon matters for which the UPC will have jurisdiction.
Such barriers to the UK's post-Brexit participation in the UPC have been very evident for a number of years now. Despite this, there have been no sightings of any remotely plausible solutions to those conundrums. Whilst an optimist might (in view of the political will behind the UPC project) still believe in the possibility that "miracle" solutions to these problems will be found, the evidence strongly suggests that such solutions do not exist.
In the light of the above, it seems that pressing ahead with the UPC in its current form is likely to result in one form of disaster or another, such as a "robust" CJEU ruling striking down the UPC (by finding the UPC Agreement to be inconsistent with EU law) ... or a "fudged" CJEU ruling that upholds the UPC Agreement but that undermines the unity and integrity of EU law. It is therefore reasonable to ask why, in view of such impending disasters, there is any political will remaining to implement the current UPC Agreement. I cannot think of any reasonable answer to this question ... and so can only hope that the judges in Karlsruhe will help to dig us all out of this hole by upholding at least one of the three substantive grounds of Mr Stjerna's constitutional complaint.