The main reason is the colonial history. Trading rights on the Gambia River were originally claimed by the Portuguese during the slave trade and then sold to the British in the late 1500s. Over the following three centuries, European involvement in Africa gradually shifted from loose spheres of influence to more clearly defined ones and eventually to formal colonization with set boundaries. During this period, the British and French struggled over control of the Gambia River but British control was solidified through the First Treaty of Verseilles and an agreement in 1889 that settled the boundaries of the French and British colonies.

Each colony then gained independence separately, Senegal from France in 1960 and the Gambia from Britain in 1965. While some did want unity between the countries, there were huge logistical barriers in terms of administration, laws, etc.

To explain in more detail, both pre- and post-independence, those governing Senegal had every reason to want control over the Gambia River, the only navigable river in the area for trade purposes. After independence, Senegal limited trade to privilege France as a trading partner, which depressed prices for exports like peanuts. The Gambia became a channel (literally and figuratively) for black market trade. If Senegal could gain control over the river, it would be easier to enforce their trade policies.

In the 1960s, the two countries commissioned a report on potential unification but nothing mich came of it, due to lack of support on all sides. Then in 1981, leftists attempted a coup in the Gambia and the Senegalese military intervened. This led to an attempt at partial unification the following year, via the Senegambia Confederation. Senegal wanted more access to the Gambia river and unity in trade policies. The Gambia wanted the protection of the Senegalese military and both countries had mutual security concerns since many ethnic groups span both countries. The confederation lasted until 1989. An inability to reach agreements about trade and the withdrawal of the Senegalese military from the Gambia (a result of conflict at the border of Senegal and Mauritania) as well as a general lack of political will on both sides caused the confederation to be abandoned.

Sources:

Boubacar Barry. Senegambia and the Atlantic Slave Trade. (Cambridge University Press, 1998)

David Birmingham. The Decolonization of Africa. (Ohio University Press, 1995)

Edmund Richmond. "Senegambia and the Confederation: History, Expectations, and Disillusions". Journal of Third World Studies. 10 (2): 172–194

Arnold Hughes and Janet Lewis. "Beyond Francophonie?: The Senegambia Confederation in Retrospect". In Kirk-Greene & Bach, State and Society in Francophone Africa since Independence. (St Martins Press, 1995)