Syrups are usually pretty shelf stable; despite of this fact, it is better, to keep most fruit syrups over longer time in the fridge; if syrups are homemade, you should always keep them in the fridge [except of your simple or rich syrup.
However this is not, what I would like to discuss in this post.
It is all about cooking...
Bartenders - or shall I say mixologists, are usually very busy to find new »wild« cocktail creations - some more advanced minds, are searching for lost and forgotten »heirloom« recipes and do revive them.
However the least bartenders are emphasizing on »produce«, other than fresh fruits and some good liquors. What about syrups?
Now - I am not a big fan of a lot of different fruit syrups. But you need from time to time good quality syrups - and if a fruit is in season, why not using it?
There are good products around. Gomme syrup of Monin is fantastic [and you don't have yourself the whole mess with gum arabica], most of the other syrups are also not bad; this is however only the case, if you don't live in the US. Apparently Monin has a French factory, which produces for most countries [all European countries, plus the Middle East, Asia...] under the strict French laws [yeah - most people don't know - but syrups have a special place in the heart of the French - as it is common, that kids there are drinking water sweetened with syrups]. These syrups are quite natural, are using sugar, no HFCS [anyways you stand to it] - you won't find preservatives in them and no artificial flavors. Unfortunately Monin serves America from their US factory, which is producing a cheaper and more industrial product [...].
Personally I really like D'arbo - an Austrian company, not only producing syrups but also jams and other fruit products - yummy.
It is apparently not hard at all, to produce your own syrup. Though there are different methods, and it is important to understand the differences.
The traditional simmering method
This is pretty straight forward and what you should expect. You are simmering simple or rich syrup and add the respective flavoring - fruits, spice(s), peels, coffee beans, you name it.
After some simmering time [depending on the flavoring itself], you let it chill down. Then you strain it.
The result: fruits are rather getting a jammy taste - which is not necessary a bad thing - but sometimes not wanted. The upside is definitely, that due to the boiling, it is pretty sterilized - that means it keeps pretty long.
The "cold infusing" method
There are some strong flavors, which don't need to be reduced as in the reduction method - but the produce is also not infused [and then taken out]. For this method you just add a respective flavoring to your rich syrup. One example is spicy ginger syrup - you just add the "juice" from ginger and the syrup will taste very strong like ginger. Despite the designation as "cold infused" it can be made with hot [or simmering] syrup and cold syrup [latter will be not as shelf stable].
The reduction method
This is rather uncommon, but a great way, to get a really rich syrup - you could rather call it fruit honey or molasses. It starts with a fruit juice, which you are reducing on low heat, until it is very thick.
The flavors are intensifying but the overall taste steers towards honey and molasses. The positive point is, that they are even more stable.
The maceration method
This method is not often used in bars [apparently I haven't seen any bartender to use this method] but it has some great advantages. You are pouring sugar over the respective "wet" flavoring [e.g. cut fruit] and let it stand refrigerated for several hours [up to two days]. The sugar is extracting the water as well as the flavor. Then you just have to fine strain the solids from the syrup [if you are using citrus zest, you have to make a simple or rich syrup from the infused sugar].
Obviously the challenge here is the time factor. The produce also has a much smaller yield and is the least shelf stable method. However: the fruit tastes fresh [or macerated] and not "cooked". I have learned about this method, when I read one cook book of Heston Blumenthal and I love to make strawberry-, peach-, pineapple-, raspberry- [...] syrup with this method.
The avant-garde simmering method
Now listen up: I just had this idea this morning. Sometimes you just would like more "stewed" aromas.
While simmering brings usually some of these flavors, you won't get caramelization - as there is too much water, as it can caramelize at 100ºC [boiling temperature of water].
However you could use a pressure cooker, which obviously reaches higher temperatures, hence you will have some Maillard reaction [browning], which leads to deeper and caramel'y aromas.
While you might not want to have this effect, if you are making some summer fruit syrups, you might look for it, if you want to make a syrup from dried fruits - or even better: ginger [ale] syrup.
Ok - this might be also not clear - but check out my post about ginger ale and ginger beer - the base syrup for ginger beer, would be the "cold infusion" method. However if you would like to have a ginger syrup, which taste rather like ginger ale, you want to have some caramelization and some "smoothing out".
At the example of ginger: clean ginger [take the peel of] and cut it into large pieces. Pour your rich syrup into a pressure cooker and add the ginger [you can also add some orange peel, celery seeds, all spice, a bit whole cinnamon etc]. Close the cooker, heat until pressure is building up and cook for 15 - 20 minutes. Let the pot cool down itself [don't release the pressure] until it can be opened.
Fine strain the syrup.
So here you have it - all imaginable methods to make your own syrups - just do me a favor - limit yourself to few, which you always keep fresh... and seasonal.