My buckle will only stay connected on one particular side first, is it faulty?

All car restraint buckles on Australian Standard restraints (any to AS/NZS 1754) use the same buckle mechanism. In Australia this is currently not a "single locking" buckle but instead requires both buckle tongues to be inserted before a complete lock is achieved.

Inside the buckle is a sprung metal plate with two pins, one for each tongue (indicated by the blue shape in the image below). This sits flat and in position when there are no tongues inserted.

When the first tongue (regardless of side) is inserted the metal plate is placed on an angle and the pin is not fully connected to the tongue. In some buckles it may hold but it won't be securely locked, other buckles will allow this single tongue to be pulled out again.

Once the second tongue is inserted, the metal plate flattens back out and the pins lock securely into both buckles, at this point you should hear an audible "click".  The buckle is now securely locked and neither tongue should be able to be 'yanked' out.

A buckle is classed as correct and not faulty by the Australian Standards, if you hear an audible 'click' when the second tongue is inserted and once both tongues are inserted neither can be pulled out.

If you cannot hear the 'click' with the second tongue, the tongues can be pulled out after both are inserted or the buckle is acting differently to when first purchased, then the buckle may need a clean, see 'Cleaning the Harness Buckle'

https://help.infasecure.com.au/hc/en-us/articles/115001899347-Cleaning-the-Harness-Buckle