In The Phantom Menace, when the lasers gates close and Qui-Gon and Maul are stuck in a section separated from Obi-Wan, why did they pause their fight and why didn't Darth Maul kill Obi-Wan while he was meditating/regaining his strength?
All three of them were separated from each other by the force fields. You can see that Maul hits the field with his saber and is forced to wait until the field opens
Here you can see the fields separating them:
The video shows the full sequence - around 120 seconds is where you see that Maul hits the field:
This is covered in the film's script. Darth Maul was unable to penetrate the laser gates. This gave Qui-Gon time to meditatate.
The SITH LORD, followed by QUI-GON, enters a long hallway filled with a series of deadly rays that go on and off in a pulsing pattern that shoots down the corridor every minute or so. DARTH MAUL makes it down several walls of deadly rays before they close. QUI-GON is one wall away from the DARK LORD. OBI-WAN is just starting into it and is five walls way from DARTH MAUL.
The JEDI must wait until the next pulse to advance down the corridor. OBI-WAN is impatient and paces, waiting for the wall of rays to open. QUI-GON sits and meditates. The SITH LORD tries to patch up his wounds.
When the gate opened, Qui-Gon was up immediately and fighting.
The electric rays cycle as QUI-GON sits meditating. The wall of the deadly rays turn away, and OBI-WAN starts running toward QUI-GON and the DARK LORD. When the wall between QUI-GON and DARTH MAUL opens, QUI-GON is in a split second fighting the DARK LORD with a ferocity not seen before. They move into the area at the end of the corridor called the melting pit, a small area that is mostly made up of a deep hole.