The dominant idea of keep is hold onto:
1.0 Have or retain possession of:
late Old English cēpan 'seize, take in', also 'care for, attend to',
of unknown origin.
The meaning of keep expands as the notion of hold onto is applied to various conditions and situations:
1.1 Retain or reserve for future use:
1.2 Put or store in a regular place:
2.0 Continue or cause to continue in a specified condition, position, course, etc.
2.2 [NO OBJECT] (Of a perishable commodity) remain in good condition:
2.3 [WITH OBJECT] Retain one’s place in or on (a seat or saddle, the ground, etc.) in spite of difficulty:
2.6 [WITH OBJECT AND PRESENT PARTICIPLE] Make (someone) do something for a period of time:
3.2 Own and look after (an animal) for pleasure or profit:
3.3 Own and manage (a shop or business):
3.4 Guard; protect:
3.5 Support (someone, especially a woman) financially in return for sexual favours:
4.0 Honor or fulfill (a commitment or undertaking):
4.1 Observe (a religious occasion) in the prescribed manner:
5.0 Make written entries in (a diary) on a regular basis:
With the preposition up, the set phrase keep up implies maintaining a comparative measure:
keep up (also keep up with)
24.1 Move or progress at the same rate as someone or something else:
The comparative measure may be explicit or implied, and it may be imposed internally or externally.
- Consider: You need to keep up, if you want to learn how to do this well.
In this example, the comparative measure is not explicitly expressed, but it is clearly implied by the result: learning how to do this well. Any comparative measure could be inserted explicitly, but one option will suffice to reveal the principle: You need to keep up [the daily dance step exercises], if you want to learn how to do this well. Also, the expression does not explicitly indicate the comparative standard.
- Consider: Keep your sales up if you want to stay within the company.
In this example comparative measure is explicitly indicated as your sales. If you eliminate the phrase your sales, the sentence becomes just like the first example: Keep ... up if you want to stay within the company. The cultural implications of employment imply that the comparative standard is externally imposed, but that is not explicitly stated.
Adding the preposition with emphasizes the comparative nature of the expression keep up, but it also tends to identify the comparative standard, as in: Keep up with the Jones', where the Jones' are the comparative standard to be maintained.
- Consider: I cannot keep up with all the reading at school.
If we eliminate the prepositional phrase, with all the reading, this example becomes just like the first example: I cannot keep up at school. Neither the measure nor the standard is identified, but may be implied.
If we eliminate just the word with, this example becomes just like the second example: I cannot keep up all the reading at school. The comparative measure has been identified, but it leaves ambiguity about the comparative standard: Are you struggling with a self-imposed reading expectation (including all the novels and magazines you read for pleasure), or is it the academic reading requirements that you cannot fulfill?. The preposition with pulls the meaning toward the academic reading requirements.
The meaning of the preposition with, indicating the the comparative standard, can be implied in the use of keep up, as in your first two examples:
You need to keep up [with your program] if you want to learn how to do this well.
Keep your sales up [with our corporate goals] if you want to stay within the company.
There is a specific application of keep up with in the OED that tends to diverge from this specific progression of meaning:
25 Learn about or be aware of (current events or developments):
Even though he’s been traveling, he’s kept up with what’s going on back home.
Keep means retain possession, and extends its meaning by application to many conditions and situations.
Keep up implies maintain a comparative measure.
Keep up with implies maintain a comparative standard.