I asked one of my former employers the guidelines he uses.
I also called the company that manufactures our chlorhexidine product and spoke with their chemist.
The short answer to your question is, we don’t really know. No one has done a study on diluted chlorhexidine over time, nor, to the best of my knowledge, have researchers ever looked at the antimicrobial effects of dilute chlorhexidine over time.
Theoretically, if properly stored, and kept from being contaminated, it might be good for some time. It of course depends on the storage conditions (light, temperature, container, storage location, use, etc). The chemist suggested that it would be best to discard any unused diluted solution after 1 day. That was just a shoot from the hip rule of thumb that she uses. This would minimize the chance of contamination and ensure maximum chemical efficacy.
If you are using it to dip foal navels, or flush wounds, I would suggest you mix it up fresh, every time. Using deionized or bottled water probably ensures maximum effectiveness and minimal contamination as well, though many dilute with just regular tapwater. The risk there is minerals in the water, or contaminants from the tap itself. Certain bacterial and fungal organisms are not very effectively killed by chlorhexidine.
If you are using it in a spray bottle as a disinfectant, you should probably change it at least weekly. Again, just a rule of thumb given to me by my former veterinarian employer that he uses in his clinic.
I hope this helps. I wish I could give you a better answer! Besides veterinary medicine, I have a degree in microbiology, and this would make an excellent project for a masters degree, and would greatly benefit veterinary medicine.