Your Experience with Reliable Connections?

[CatalinaWOW]

You might look into the plastic circular connectors from TE connectivity.  Relatively inexpensive and have most of the features that make the MIL-SPEC and very expensive connectors good.  I have had good luck with them, but have not used them in a severe environment.

The other thing to think about is to do what the serious players in the reliability game do - they test their approaches, both in the design phase to find weaknesses but often also in assembly/fab to weed out latent failures/manufacturing defects and the like.  Some of the early work on this was gathered by a guy named Willoughby, a google search on Willoughby templates will bring up a lot of good history and material.  While the details of implementation have in many cases moved on from Willoughby the concepts are good.

Doing this quantitatively with calibrated vibration stands and the like is difficult and expensive.  There are many traps and it requires a lot of knowledge and experience to do it right.  But a qualitative form is relatively easy and can rapidly find the weak points in your approach.  Something as simple as an eccentric wheel driving a platform with a couple of loose weights that can bang a bounce around can do the trick.  Again, a google will find ideas and concepts.   Just be aware that there are two serious risks in the qualitative approach.  First, you may be under stressing your UUT, and will find more defects in the field, just as you are currently.  Second, you may be overstressing, and consuming the life of your unit or outright destroying it needlessly.

You can try to split the difference between the qualitative and quantitative approach by doing the instrumentation you can afford on your device in a competition.  Shock sensors, accelerometers and the like.   At affordable levels these will be poorly calibrated, limited bandwidth and have other problems.  But they can give a rough idea of the correct environment, and you can compare that with what you see on your banging/clanking screening machine to find if you are in the right order of magnitude (or two, these things are really tough to nail down).

[TimFox]

I like the "CPC" connectors mentioned here, especially the lower-density ones that are rated for higher voltage.  The locking collars work very well.
One thing to watch out for, however, is that sometimes you don't insert the barb-locked pins far enough;  then they get pushed back when the connectors are mated.  Test each one individually by pulling on the wire after insertion.

[Maxoverdrive]

whatever the connector family you will selected , a matched crimp tool is mandatory and crimp tools are generally costly tools , that a parameter to check before to select a model of connector , other solution is hollow base with solder as MIL-DTL-26482
Some mil connector as MS3111 can be very reliable they are available in true Mil specs and industrial specs which are far affordable in price .