The AMA safety rules for Control Line has a section requiring a safety thong which ties the handle to the pilot's wrist be worn at all times except for racing events. You may let go of your model but your model isn't letting go of you. The following text is from the AMA Competition Rules book:

Control Line General
4. Safety Thongs. A safety thong connecting the handle of the Control Line models to the pilot’s wrist, and strong enough to prevent accidental release of the model, shall be worn during all flights of Control Line events except all Racing events. The safety thong should have a minimum amount of slack to preclude accidental release or interfering with the controls. Releasing the controls during flight or before the model has come to a complete stop shall constitute a foul if the safety thong restrains the model and lines from flying free; if the contestant releases the controls and the safety thong during flight or before the model has come to a complete stop, the contestant shall be barred from further participation in the event and all of his previous flights canceled.

In those events not requiring the use of a safety thong, releasing the controls during flight or before the model has come to a complete stop shall bar the contestant from further participation in the event and void his previous flights in the event. The safety thong may be a point of attachment for conducting the pull test or the thong may be tested separately from the test of control handle, lines, and control mechanism.

When the thong is tested separately, it must be pulled to the test load specified for the particular model involved. The method of thong attachment shall also be able to withstand the required pull test. Failure to use a safety thong in those events for which they are required shall constitute a foul.

Although safety thongs are optional in Racing events, their use is encouraged in all events, particularly when Junior and/or Senior fliers are involved.