Gracias a un pequeño préstamo estudiantil, mi hermana terminó la carrera sin tanta deuda.

In this structure, gracias a works like “thanks to” in English and introduces the cause or means that made something possible.

• Gracias a un pequeño préstamo estudiantil…
  = Thanks to a small student loan… (that loan made the result possible)

By contrast:

• Gracias por el préstamo = Thank you for the loan (you’re thanking someone for something directly)
• Gracias a + noun / verb = “thanks to” (it introduces a cause: Thanks to X, Y happened)

So here we’re not thanking a person; we’re explaining why she finished her degree with less debt, so gracias a is the natural choice.

Most of the time, yes, gracias a suggests a positive or at least neutral cause:

• Gracias a mi jefe, encontré este trabajo.
  Thanks to my boss, I found this job.

However, in real usage people also say it with negative things, often with irony:

• Gracias a tu despiste, llegamos tarde.
  Thanks to your absent-mindedness, we’re late.

So grammatically it just links a cause and a result. Context and tone tell you whether it’s sincere or ironic. In your sentence it’s clearly positive: the loan helped reduce her debt.