Submit the neurologists recommendation to the school district and cite no improvement. You have the right to request an emergency IEP at any time you feel necessary. Always do so in writing, however, they do have response period that differs by state- but it is generally is calculated in school days (Christmas break stops the clock). If you have behavior issues- capitalize on it and request ABA- they can help with behavior and work on speech goals- manding for information, socialization, etc. It's a work around and sometimes you end up with better results. School speech is not always great. Remember the GOALS DRIVE YOUR SERVICES. Sit down and really come up with a thorough definitive list. It's not enough to say you want more.
You can start fighting the insurance company for services- long road but worth it- (it took two years for me to get services I requested from them.) We requested services, were denied (repeatedly)- you then submit an appeal through Department of Managed Health Care that rule on the case- 90% of the time in the patients favor. I made headway by pointing out my son's speech and fine motor delays were linked to autism- a neurological disorder- which is a medical condition. They treated MS, Alzheimer's, and even alcoholism- all neurological disorders- why were they discriminating against autism? Be a squeaky wheel- call the paper, the news, your congressman. Many states are forcing insurance companies to provide these services to their patients. What is your congressman doing for you and where do they stand? Be polite but persistent.
Sometimes it's the parents that stand up and say "No, that is not acceptable." that help others without even knowing it.
Fight for your child's rights.

We started special services for our Son at 3 years old, call your district and call for a review. Whenever the district was dropping a service like speech, we would get a letter from our psychiatrist that was treating him or take him for a review to a speech pathologist. Once they write a report recommending speech work more often for address deficits, the school would implement it again. If you believe your child needs the service, fight for it. We are the advocates for our children. The school is looking to their budget.

My son is 9 now, so I don't remember if the IEP process at the pre-K stage will let you add it in more speech therapy. We had a similar situation.

Have you looked into the Katie Beckett or similar waivers?

Also, it might help to have the neurologist provide you with a written recommendation for a specific number of hours of speech therapy that they feel are required to help your son make progress.

Thanks for all the help!!! My son does have an IEP in place from what I hear. I just got the application for the waivers and starting that process. I was told we can get medicaid and one other. I intend to apply in person, thought that would be better than online. Have heard stories about people getting bumped from the waiting list so I will be diligent in checking.