Saving was something we frequently looked into during development but ultimately decided against for a number of factors.
During playtests players quickly became over reliant on reloading saves rather than rebuilding their tower’s base (which was often the source of the problem). This led to their tower collapsing over and over again due to a design flaw made before they saved. This often caused playtesters to assume the game was impossible or rigged. Unexpectedly it was almost always faster for players to rebuild after a collapse than to fiddle with saves.
This is something that many other tower builders with levels that last considerable length have in common with us, either having no ability to save or an unorthodox method with mixed results (World of Goo time flies are an example of this).
The final reason being that the reward for completing Pit of Babel requires real world work on the behalf of Scottie and I, and the ability to save lead to such a wide variety of exploits we would either have to remove the reward from everyone or invest in significantly more infrastructure than is realistic for a game jam.
If there was a clean solution to saving the players progress that did not cause more problems than it solved we would have taken it. Unfortunately no solution seems to have arisen for Pit of Babel or other similar tower builders.
-Maceo