Twice this season I have been #1 on an international player only to have them sign with another team without any notice that I have been outbid.. Is there a certain amount of time from when the player is posted to the time he will sign where no further opportunity to bid is given?
Are there any other reasons this would happen? Thanks

Short answer: yes, there is a time frame for a signing deadline, which varies slightly for each player. And whether or no you'll get a chance to respond to a higher bid depends on how much you've been beaten by and how close you are to the deadline.

Long answer: here is the answer from the help menu.

"When an international prospect receives his first offer, his negotiation timetable is outlined. This means that he will make a decision on which offer to accept no later than date X. As he receives offers during that timeframe, his chance of accepting an offer increases the closer he gets to date X. This means that the chance of him and his agent informing other franchises of better offers is higher earlier in the process. This varies from player to player, agent to agent. Some are more patient and will drag the negotiating cycle to the end. Others will be more impatient and accept an offer more quickly. Each negotiation is different, although most follow the same pattern of back and forth negotiating until a decision is made. Furthermore, when a player receives an offer that is significantly higher than his other offers on the table, this also increases his likelihood of making a quick signing."

  Thanks a lot. Can you read anything into the replies other than having the best offer or not? For example does the wording hint to how far behind your offer is, or how long he might wait, etc.

No, not at all.

You have two choices: 1. Keep getting eaten by the sharks, or B. Learn to become a shark.

...or 3. Stay out of the water.

He's gonna need a bigger boat.

"Can you read anything into the replies other than having the best offer or not?" 

Sometimes the replies appear to indicate the number of bidders ahead of you (one versus multiple).  If you're behind multiple other bidders, I assume it's an indication that you're significantly underbidding.  

I wouldn't assume that.

I assume the content of the replies is entirely cosmetic.  I mean, "Homey don't wanna ride around in a Yugo"... ?

It means he literally doesn't want to ride around in a Yugo.