GLP-1 receptor agonists may be administered repeatedly or continuously for prolonged periods of time to human subjects with type 2 diabetes, hence the question of whether patients will gradually exhibit a diminished therapeutic response to GLP-1R activation has direct therapeutic relevance. 

Incubation of islet cells with native GLP-1 induces rapid GLP-1 receptor desensitization , as shown in Homologous desensitization of the insulinotropic glucagon-like peptide-I (7-37) receptor on insulinoma (HIT-T15) cells. Endocrinology. 1991 Jun;128(6):2880-8 and Desensitization of glucagon-like peptide 1 receptors in insulin-secreting beta TC3 cells: role of PKA-independent mechanisms. Br J Pharmacol. 1996 Jun;118(3):769-75

GLP-1 receptor desensitization is accompanied by phosphorylation of serine residues in the carboxyterminal tail of the receptor Desensitization and phosphorylation of the glucagon-like peptide-1 (GLP-1) receptor by GLP-1 and 4-phorbol 12-myristate 13-acetate. Mol Endocrinol. 1996 Jan;10(1):62-75 and Internalization and homologous desensitization of the GLP-1 receptor depend on phosphorylation of the receptor carboxyl tail at the same three sites. Mol Endocrinol. 1997 Jul;11(8):1094-102.

Heterologous desensitization of the islet GLP-1 receptor was also observed following acute exposure to PMA however these studies also demonstrated that GLP-1R desensitization in islet cells may involve mechanisms partially independent of PKC and PKA Desensitization of glucagon-like peptide 1 receptors in insulin-secreting beta TC3 cells: role of PKA-independent mechanisms. Br J Pharmacol. 1996 Jun;118(3):769-75

Baggio and colleagues compared GLP-1 receptor desensitization in islet cells following incubation with either GLP-1 or exendin-4. Both GLP-1 and exendin-4 produced homologous desensitization. Exposure of  INS-1 cells to epinephrine, GIP, or glucagon did not produce heterologouse GLP-1R desensitization. Nevertheless, incubation of INS-1 cells with exendin-4 was associated with a greater degree of GLP-1 receptor desensitization compared to comparable incubations with GLP-1 as described in Chronic Exposure to GLP-1R Agonists Promotes Homologous GLP-1 Receptor Desensitization In Vitro but Does Not Attenuate GLP-1R-Dependent Glucose Homeostasis In Vivo. Diabetes. 2004 Dec;53 Suppl 3:S205-14. Given the greater stability and prolonged activity of exendin-4 relative to native GLP-1 it seems likely that islet cell and extrapancreatic GLP-1 receptors would be exposed for a greater period of time to intact degradation-resistant exendin-4. Nevertheless, transgenic mice expressing a MT-exendin-4 transgene do not exhibit significant diminution in their responsivity, as assessed by analysis of glucose homeostasis, to rechallenge with exogenous exendin-4 Chronic Exposure to GLP-1R Agonists Promotes Homologous GLP-1 Receptor Desensitization In Vitro but Does Not Attenuate GLP-1R-Dependent Glucose Homeostasis In Vivo. Diabetes. 2004 Dec;53 Suppl 3:S205-14.Furthermore, patients treated with twice daily exendin-4 for 30 weeks continue to exhibit a reduction in HbA1c and exhibit marked reductions in postprandial glycemic excursion even at the end of the 30 week study Effects of exenatide (exendin-4) on glycemic control over 30 weeks in sulfonylurea-treated patients with type 2 diabetes. Diabetes Care. 2004 Nov;27(11):2628-35. Hence there is little evidence to date that the GLP-1 receptor undergoes "clinically" meaningful desensitization in vivo.