How does the brain avoid feedback loops?
Normally, after an excitatory neuron fires, it becomes more resistant to firing again for a period of time (refractory period). This is due to electrical changes within the excitatory neuron.

After depolarazing and reaching an action potential(firing), the neuron enters the refractory period, in which its charge will go back to normal (resting potential). This refractory period can be divided in two phases: Absolute and relative. During the Absolute refractory period, the neuron cannot be discharged again, since the sodium channels are inactive. 

It's the relative refractory phase, however, that is more relevant to your question. During this period, the neuron enters a hyperpolarization states, meaning that it's resistant to firing again, unless it receives a greater stimulus.

So, basically, after firing and for a while, a neuron requires greater stimulus to be fired again. This works as a Feedback control, since even if you overstimulate a neuron it can fire only so often. 

Inhibitory and excitatory neurons (and inhibitory and excitatory neurotransmitters) also play a role in the feedback control. Inhibitory neurons reduce the likelihood of a postsynaptic neuron to fire while excitatory neurons do the opposite.



However, sometimes these mechanism fail. 

For instance, in Epilepsy, the resistance of excitatory neurons to fire during the refractory period is decreased. A group of neurons begin firing in an abnormal, excessive, and synchronized manner, resulting in a wave of depolarization known as a paroxysmal depolarizing shift, causing seizures.

In Parkinson disease, decreased dopamine causes increased inhibitory output (excess negative feedback) of the motor circuit, which leads to hypokinesia.

In contrast, excess dopamine and dopaminergic neuron activity seem to be related with Schizophrenia.