There's no "magic number". The only way to avoid spam, is to not list it in your directory. That means you have to first know how to identify it, then you need to reject/remove it.
It depends on the nature of the links some time we can approve more than 100 links but some time we do not approve any link it all depend on the content of the web and nature of the keyword density of the link submission directory.
I have experience when doing link building, I have submitted one primary domain but when I am about to submit the said domain a prompt said that I have submitted the site already. What could be wrong about it?
There is no specific rule but roughly, in the start (if your site is new) go with a number around 3-4 a day and as your site gains traffic you can increase these numbers.
Do only 5 -6 submission per day but submission should be quality base and don't do submission on bulk as it considers as a spam and over optimization. There is no limit of submission per day as if not to do submission 50 per day as if you never know how many submission will be approved. To avoid spamming do quality link in less numbers and quality backlinks ever last for dayz
In order to avoid spaming always try to use quality work with effective strategies. If your content is unique(don't copied) make sure 3-5 link at daily basis are helpful for you website.
I will be agree with the reply of mangobuddy. No matter....how many links you approved, but they should be of quality...............