By the way, I just read the following on the internet, and my Dr. also told me to stop the Clonidine gradually and don't stop all at once.

Do not stop taking this medication without first consulting your doctor. Withdrawal reactions (e.g., nervousness, agitation, shaking, headache) and a rapid rise in blood pressure may occur when the drug is abruptly stopped. The risk is greater if you have used this drug for a long time or in high doses, or if you are also taking a beta blocker (e.g., atenolol). There have also been rare reports of severe (possibly fatal) reactions from stopping this drug too quickly (e.g., stroke). Therefore, it is important that you do not run out of clonidine or miss any doses. Tell your doctor or pharmacist immediately if you are unable to take the medication (e.g., due to vomiting). If you must stop taking this drug, your dose should be gradually decreased over several days as directed by your doctor.

When used for a long time, this medication may not work as well and may require different dosing or an additional medication. Talk with your doctor if this medication stops working well (e.g., your routine blood pressure readings increase).