We show that Born-Oppenheimer surfaces can intrinsically decohere, implying loss of coherence among constituent electronic basis states. We consider the example of interatomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultracold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by continuous monitoring of the dimer state through a detection scheme utilizing the background gas atoms. We show that this intrinsic decoherence of the molecular energy surface can gradually deteriorate a repulsive dimer state, causing a mixing of attractive and repulsive character. For sufficiently strong decoherence, a Zeno-like effect causes a complete cessation of interatomic forces. We finally show how short decohering pulses can controllably redistribute population between the different molecular energy surfaces.