The documentation for static maps states:
URL Size Restriction
Static Map URLs are restricted to 2048 characters in size. In practice, you will probably not have need for URLs longer than this, unless you produce complicated maps with a high number of markers and paths. Note, however, that certain characters may be URL-encoded by browsers and/or services before sending them off to the Static Map service, resulting in increased character usage. For more information, see Building a Valid URL.