Why did the foreigners invade deeper into Roman territory?

Because Their military was not as strong as it used to.

Explanation:

The kings of Rome often had a lot of children. In a lot of cases, these kings decided to divide the empire into several parts and give each part to their children when they grew up. Since this happened over several generations, Roman territory keep getting smaller and their military forces started to became divided.

Foreign invaders saw this as an opportunity. They have no chance defeating the Romans when they're at the peak of their power. But things became a lot of easier after they're divided.

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