Do people still travel to and from Vers after Heaven's Fall?
We found out right at the beginning of episode 1 (around 0:22) that Asseylum herself left Vers just two months before the start of the show, at which point she is in Earth orbit (in Cruhteo's castle). Also, in episode 21, we see that Klancain (Cruhteo Jr.) has come from Vers to meet Slaine.

So transit from Earth-vicinity to Mars without the Hypergate surely must be possible, but this of course says nothing about how prevalent it is. 

I suppose this also does tells us one more thing - the fastest mode of transit from Mars to Earth orbit must take somewhere under two months, which is considerably faster than all currently proposed ways of getting people to Mars. 



If we want to look to marginally-less-canonical material: the second volume of the BDs came with a short manga titled "Aldnoah.Zero Extra Episode 01", which portrays Slaine's life right after the passing of his father, including his being taken in by Cruhteo. 

Here, we learn that the Orbital Knights (or at least Cruhteo) and their retinue come to Vers every so often on business. 


  
  
  Top left panel: Asseylum asks Cruhteo, "You had come to Vers?"; bottom right panel: Cruhteo replies, "I had a minor matter to attend to."