Hi, Steve. I scheduled this appointment ‘cause it has been a while since we touched base.为什么要有个base？
Hi, Steve. I scheduled this appointment ‘cause it has been a while since we touched base.最后为什么要有个base？直接说Hi, Steve. I scheduled this appointment ‘cause it has been a while since we touched.不就行了吗？

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If you're asking which is correct, the first one means it has been a long time since you contacted each other and had a chance to exchange updated news/information.  "To touch base" is an idiom that means this.  Saying "... it has been a while since we touched" means that you want to physically touch the other person in a romantic or sexual way: by eliminating the "base," you are now using the literal meaning of the verb "to touch."

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Since we touched不严谨啊，至少也应该是since we got in touch.

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