How long do they keep the remaining half of the syringe when lip injections are done?

We
do not "save syringes." Patient
safety is a primary concern. The syringes
are labeled single use only.
FDA’s
statement: injectable gel is packaged for
single patient use. The contents of the syringe are sterile and non-pyrogenic.
Do not re-sterilize. Do not use if the package
is opened or damaged. As with all transcutaneous procedures, dermal filler
implantation carries a risk of infection. Follow standard precautions
associated with injectable materials.
FDA’s
statement: injectable gel is to be used
as supplied. Modification or use of the product outside the Directions for Use
may adversely impact the sterility, homogeneity, and performance of the product.
The
training and safety measures are of the utmost importance. Choose a Board
Certified Plastic surgeon, Board Certified Dermatologist, Board Certified
Facial Plastic Surgeon, Oculoplastic surgeon, or Certified Aesthetic Nurse
Specialist.
Ask questions!!

There really is no official answer on this.  It depends upon the comfort level of the injector as to how long to save opened syringes.  I do not like to save them for more than 8 weeks.