I've been using the same syringes for months now. I replace them regularly, but it is okay to reuse them provided you follow some common sense precautions when you're mixing juice.
1. Use hot water and soap and rinse often. This is especially true if working with menthol, I find that it can and will recrystallize in the syringe.
2. If using the same syringe to add nic rinse thoroughly before putting it into vg, pg, or flavorings. This is so you don't accidentally contaminate the pg/vg/flavor with the nicotine (or it will throw off your mg/ml target...not so important to me, as I actually use a funnel and small beaker for large batchs containing nic, and as long as I'm "close enough" on the nic I'm fine).
3. Wash and rinse the syringe when playing with flavoring agents. The Principle of cross contamination and why it is bad should be self-evident.
4. Place transparent tape on the writing on the syringe, it will lengthen the life of those measurement markings.
If you have a large bowl or several you can set up your wash/rinse station near your mixing area. This is what I do, but I have a lot of spare kitchen type equipment laying around my house anyway.
That said, syringes are relatively cheap to buy and if you really want to you can use new everytime. Personally I have a menthol syringe that is solely used with menthol drops and nothing else. Otherwise I use the same syringes over and over.