You should contact a local attorney about possibly bringing a lawsuit against the neighbor and possibly against the landlord. An attorney will need to know about the damages that you have suffered - medical bills, doctor bills, etc. as a basis for a lawsuit.
The information provided in this answer does not create an attorney-client relationship. If you are interested in his legal services, feel free to call Chris at (303) 409-7635 at his law office in the Denver Tech Center. All initial consultations are free of charge.
No one can "force" you to drop a case. Have you called animal control and/or the police? You need to be way more proactive about this; I agree with my colleague that you should speak with a local attorney regarding your options. The Colorado Bar Association can give you a referral: www.cobar.org
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
I agree with what the previous two posting attorneys have written. The Colorado attorney you contact likely will instruct you to retain copies of all the veterinary expenses you have incurred. In addition, he/she may want to know more about the facts surrounding your landlord forcing you to drop your case. Be prepared for that.
For now, until things change, I suspect you will have to be cautious to keep yourself safe. Has animal control been contacted? Good luck with whichever Colorado attorney you select.