Anytime people talk about "pain clinic" this issue keeps coming up. For a reason, unbeknownst to me, patients are expected to submit themselves to needling. Often these injections are performed weekly yet providing either no or very short-term pain relief. For the sake of argument, a placebo effect will not be discussed here, although, indeed there is a lot to do with the so-called expectations and other behavioural effects.
Physiologically, injected local anesthetics (hopefully, without corticosteroids) produce some pleasant warming numbness and muscle relaxation. Rarely, they offer long-lasting pain relief, but the mechanism is not clear. We can speculate that when these drugs are injected very close to the target nerve, or into the nerve, they cause neurotoxicity (poisoning) and slowing conduction of electric impulses through this nerve. There is another hypothesis of a so-called "pain reset," some magical Microsoft-like solution: if something doesn't work, and you don't know what to do, just click "restart." There is also a strong belief that with repeated nerve blocks, the pain will be diminishing. All these hypotheses have never been experimentally confirmed. On the other hand, tissue toxicity was documented in laboratory studies, and conscientious, ethical pain physicians published their experience disproving nerve injections (Arne Johansson and Bengt Sjolund. J Pain Symptom Manage 1996).
On the other hand, nerve blocks can be extremely helpful to identify “pain culprit”. These injections are done to temporary freeze small sensory nerves conducting different feelings including pain. For example, chronic low back pain may be related to intervertebral discs, supportive joints (facets) or other non-spinal structures, such as the sacroiliac joint. Anesthesia of these nerves helps doctors to determine the pain source. Once the diagnosis is made, a more definitive procedure can be considered.