The Washington Post has an article by Edward Walsh, Redrawing Districts Raises Questions; No Precedent Seen for GOP efforts. (There’s also this related article on Texas redistricting.)
The article considers the constitutionality of the practice that took place in Texas and Colorado to do a second redistricting in a single decade. Multiple redistrictings have been done in a single decade before, but for purposes of remedying a constitutional or Voting Rights violation. These redistrictings were done for partisan (in this case, Republican) advantage.
Under what theory might re-redistricting be unconstitutional? According to the article, “[i]n a lawsuit filed in U.S. District Court in Tyler, Tex., [Democrats] note that the Constitution requires that House seats be reapportioned among the states after each 10-year Census. An ‘implicit assumption’ of that reapportionment mandate, the Democrats argue, is that the redrawing of district lines within states will take place on the same schedule.”
The Democrats’ lawyer, Sam Hirsch, further explains in the article:

“All we’re saying is that implicit in decennial reapportionment is decennial redistricting,” said Sam Hirsch, a lawyer for the Texas Democrats. “American constitutional law is full of implicit assumptions. The idea that reapportionment and redistricting are tied together is a small inferential leap. The reason is that reshuffling districts every two years undermines democratic accountability. People should be able to vote for representatives who served them well and against those who have not served them well.”

I think this is another unfortunate example of losers in the political process looking to courts to create new substantive rights in an effort to achieve a result that cannot be achieved politically. It is more than a small inferential leap to go from constitutionally mandated apportionment to a constitutional cap on the number of redistricting in a decade. The Constitution requires the decennial reapportionment to make sure the representation among the states is proportional to the population of those states. The principle at work here is one of equality or fairness across the states. It has little to do with accountability.
It would be a big leap for a court to say that because we must apportion every ten years, we may not redistrict within an apportioned state more than once a decade. Such a rule does nothing to further the goals of reapportionment.
I agree with Sam and with Tom Mann (quoted in the article) that multiple redistricting in a single decade is a bad thing, not only on grounds of accountability but also on grounds of political instability. And legislators focused on redistricting battles–such as legislators in Texas–can hardly concentrate on legislative business. But the solution then is to do as some states have done and forbid the practice of re-redistricting in a single decade. In those states that have an initative process, such a change could be enacted without legislative approval. In other states, it would be a tougher battle, most likely to be enacted when either Democrats or Republicans can see themselves on the wrong end of a re-redistricting in a finite time horizon.
But there are real costs to constitutionalizing policy choices like this, both related to further enmeshing courts in the political process and further removing options for future experimentation by states in ways that may be unforeseen today.
That’s not to say that the Texas re-redistricting is legal. It could violate the Voting Rights Act or have some other problem. But I don’t see creating a new constitutional right here.