Why did the United States under the Articles of Confederation have a hard time getting funding?

Request vs Demand

There is a difference between a theoretical right, and the practical ability to exercise that right. In theory, you are correct that the Confederation Congress was empowered to set tax quotas and due dates for the States.^[1] In reality however, Congress had no actual means of enforcing this.

Under the Articles of Confederation, extractive capacity was severely limited, and neither legal authority nor bureaucratic machinery existed to enforce the demands of the Continental Congress for revenues.

_{- Forsythe, Dall W. Taxation and Political Change in the Young Nation: 1781-1833. Columbia University Press, 1977.}

It is not particularly meaningful to examine the word choice of demand or request by different writers. Congress could demand whatever it wanted: the issue was that when the States ignored it, Congress had little recourse aside from begging.

Collectively, the states contributed merely thirty-seven percent of the amount they were supposed to send to the Congress. Once it became clear to the state governments that they could free ride without suffering punishment, the problem only worsened.

_{- Strahilevitz, Lior Jacob. "The Uneasy Case for Devolution of the Individual Income Tax." Iowa Law. Rev. 85 (1999): 907.}

Unpaid Requisitions

Strictly speaking, therefore, the States were legally bound to pay their requisitioned quotas. In practice this view was not universally shared. For instance, Rhode Island delegates Jonathan Arnold and David Howell wrote home in 1782 that:

You are, at the same time, to be informed what has been done, with your last quota, and, on a full consideration of the representation so made to you, you are to grant your money like freemen, from time to time, bound only, as a sovereign and independent State, by your sentiments of justice, of virtue, and by your sacred honor. This is the voice of the Confederation.

_{- Staples, William R. Rhode Island in the Continental Congress. 1870.}

More practically, the early America republic was designed around the idea that virtuous people would make sacrifices for the public good.^[2] On the issue of taxation at least this quickly fell apart. While States made genuine efforts to meet their obligations, this did not last long.

As states failed to pay their requisitions, the New Jersey Assembly, and other state legislatures, became increasingly reluctant to pay their share ... States failed to pay their requisitions because they lacked resources. But they also failed to pay because they did not want to carry the nation's fiscal burden alone nor to allow their neighbors to pay less than their fair share ... states were unwilling to surrender local interests for the good of the whole.

_{- Dougherty, Keith L. Collective Action under the Articles of Confederation. Cambridge University Press, 2006.}

Essentially, whether the quotas are paid on time (or indeed, at all) depended on the voluntary compliance of the States. This was not always (or usually) forthcoming.

The Articles of Confederation deliberately engineered a weak central government. Congress could neither coerce the States into paying, nor punish them for their failure to do so; and its attempts to remedy the situation were easily thwarted. Proposals to realise a revenue from tariffs were single handedly shutdown by Rhode Island, for example.

Ultimately, the confederation was in a state of financial disrepair because it was so weak.

Notes:

^{[1] "No state can dispute the obligation to pay the sum demanded without a breach of the confederation ... Such a refusal [to comply] would be an exertion of power, not of right." Continental Congress, Committee of the States. Journals of the Continental Congress. Way and Gideon, 1823.
[2] "The authors of the American confederation created a system that depended on individual commitment to the common good and some sense of self-abnegation. They assumed that patriotism and civic duty would encourage states to comply with requisitions and to make their confederation work" Dougherty, Keith L. Collective Action under the Articles of Confederation. Cambridge University Press, 2006.}