Let's clear up a misunderstanding. ESTA is permission to get on a plane. It's valid for several years, and you can do several trips to the USA on one, application. ESTA does not admit you to the US. The rules that limit how long you can stay in the US are the Visa Waiver Program (VWP). This is important because reading up about 'renewing an ESTA' will not give useful information if you are looking to find how long you can stay in the US.
So to give the trivial answer to the question you asked, no you don't not need a new ESTA. Your original will serve you for a few years. But that's not important. The VWP is important.
If you enter the US in the VWP, exit to Mexico (or Canada or the Carribbean) and re-enter, you do not get a new VWP admission. You are readmitted under the original. You have to leave the US within 90 days of your original entry to the US.
If you were given a green I-94 form (record of admission under the VWP), you should keep it when you leave to Mexico, and re-present it. If you were dealt with electronically then you arrivals and departures will be recorded properly.