What happens if we continuously stimulate a mimosa plant?
Mimosa leaves have mechanoreceptor cells which sense the mechanical stress through proteins called mechanoreceptors (they are similar to the ones responsible for sense of touch in animals). When stimulated the mechanoreceptors cause ion channels to open leading to depolarization. This generates an action potential (AP; like neurons) which in turn activates the motor cell (Visnovitz et al., 2007). Motor cells cause leaf movements by change in their interior turgor pressure (similar to opening and closing of stomata). 

Repolarization (like in neuronal AP) takes time and Mimosa would not respond to stimuli that are too frequent. The time required for the turgor pressure to relax would be an additional factor.

I am no plant biologist but if I compare this situation with that in neurons, I can speculate that long term non-responsiveness similar to LTD may happen because of down-regulation of mechanoreceptors. It has actually been shown that Mimosa does actually become insensitive to a persistent stimulus such as a continual water drop and moreover exhibits a long-term "memory" of this non-responsiveness (Gagliano et al., 2014). However, the exact molecular mechanism has not been elucidated. Again, there would be thresholds (on amplitude and frequency) for the signal to elicit these kind of changes.


 

References


Visnovitz T, Világi I, Varró P, Kristóf Z. Mechanoreceptor Cells on the Tertiary Pulvini of Mimosa pudica L. Plant Signaling &amp; Behavior. 2007;2(6):462-466. 
Gagliano, Monica, et al. "Experience teaches plants to learn faster and forget slower in environments where it matters." Oecologia 175.1 (2014): 63-72.