The Venezuelan government announced that Hugo Chávez will invoke article 231 of the constitution and swear in at some unspecified later date. The letter they cite is from Vice President Maduro, not from Chávez, which means he is physically and possibly mentally unable even to write.
And what does Article 231 say?
Artículo 231. El candidato elegido o candidata elegida tomará posesión del cargo de Presidente o Presidenta de la República el diez de enero del primer año de su período constitucional, mediante juramento ante la Asamblea Nacional. Si por cualquier motivo sobrevenido el Presidente o Presidenta de la República no pudiese tomar posesión ante la Asamblea Nacional, lo hará ante el Tribunal Supremo de Justicia.
OK, so now we parse. It does not say you lose the presidency if you are not sworn in on January 10. It only says you need to do so in front of the Supreme Court. I would take that to mean on that same day, as I wrote before, but it does not specify that.
In other words, it is a stretch about the spirit, but falls within the letter of the constitution, especially since he has legislative approval to be outside the country. When you're referring to a president, though, spirit matters. What Venezuelans are being told is that their president is so incapacitated that he cannot be seen and cannot write, but that they should just trust spokespeople who have been lying constantly (while demonizing those who spread rumors because the government provides no facts!).
Even if you admire Chávez, this should trouble you because it is no way to govern. It is almost exactly one month since the president has communicated directly with his country. Is there precedent for that? If so, my guess is the comparison will not be complimentary.
So it's not unconstitutional. Yet. But we don't need constitutional articles to tell us that presidents need to show evidence they can continue governing. Hiding in Cuba and lying to your nation is really the definition of the opposite.