First and foremost let me say that I have rooted cuttings easily in the past using just simple cuts, rooting gel, coco+perlite mixes and dome and got most of them to root. But when things go wrong it can be a number of things and the only way to work it out is to go into hospital mode. Really this is a question of how you solve biological problems, you can do it the hard and fast economical approach ie what am i loosing and how much will it cost for me not to loose it, and how much will i benefit from not loosing it, or play with systems like airoponics and such. I myself am a hobbyist and am also inclined to play with new toys, but just know you dont have to spend a bomb in order to do this. Infact i've been to commercial nurseries who do this in the thousands for veggies in unsterile soil mixes and plugs almost 0 cultural preventative practice have 1% loss, but they use chemical fungicides.
Generally what actually kills your cuttings or seedlings is fungus. A number of factors contribute to allow the fungus to develop and infect your cuttings. The environment that cuttings require is for one ideal for the fungus to take hold, that is a damp substrate, humid atmosphere and wet leaves. Combine that with stress (wilted/damaged leaves and such) and wounds and you have a prime candidate for fungal infection.
(1) If you can keep contaminants out, you are cheaply and drastically lowering the probability that they will infect your already suffering cuttings. Sterilising your cutting tools, trays and dome with a light bleach wash is a good idea. Using a pathogen free substrate is also a good idea. A number of seedling mixes can claim this, but you can also use substrates like perlite or rockwool which you can use a typical light hydrogen peroxide solution when you wash it. The barrier not only acts as a means of keeping humidity up to preventing spores and other dormant forms of fungi and bacteria from entering. If you have access to soft water from the tap, chlorine enures its pathogen free, if you have hard water try RO, demineralised or just bottled water. Always always always use water you know is pathogen free. When handling the cuttings, wash your hands before with an antiseptic/antifungal/antibiotic soap or better yet, use sterile gloves.
If the above doesn't work or you're abit lazy, i know that some commercial nurseries use preventative fungicidal applications, though this is not a common practice with weed, not one i've ever needed to use at least. I can't think of any organic preventative fungicides that would work on cuttings as i suspect copper based solutions maybe to hot and limited to leaf rot. There are a number of systemics that work through foliar or watering that work against root, stem and leaf rot. This is a line of inquiry you'd need to speak to a commercial agricultural supply shop or similar.
(2) Take a good cutting. This is usually a growth tip, 2-4 leafs are about right. I like to leave 2-4 leafs and cut the leaf to half, but this is a matter of preference and the leaf profile of the cutting you have taken. The idea is to leave enough leaf area to allow expire only as much water as it can absorb, to prevent wilting and stress that fungus likes. Your plant has to breath well. Dip it in rooting hormone, it will speed up the process and improve your odds. Also temperatures have to be around room temp, i dont get too fussy about this, if im comfy in a tshirt without being hot, then thats about right, it should be warm enough for the humidity not to condense is the jist.
(3) Your substrate has to be moist, but not wet all the time, again a good airy mix will make it harder for fungus to take hold on the stem and new roots. I like a perlite-coco mix and things like aircloners people mention make sense too as alternative solutions to the same problems. The coco i use is pre-treated to be pathogen free. No two substrates are ever the same from different suppliers (sometimes even the same) so while it might work for me it might not work for you, or it might not always work is more like it
(4) Watering is important, use a fine mist 1.5L sprayer, the finer the better. Spending a little more is worth it when it comes to this, as you'll use it time and time again. Also water the substrate to keep it moist but not wet. I guess misting 1-2 times a day is about right, watering, probably every other day, but again this is a function of your environment and containers. Avoid fertilizers, until you can see roots at the bottom of the plug or the the cut looks like its rooted and its getting hungry (yellowing or chlorosis). Again what you use is a mater of preference, you can buy a preformulated one for seedlings, or just give them a 10% foliar application of your base npk regimen. Again, remember, clean water.
I think that about sums it up !