If you have the plugin on a shared hosting server and experience lots of times / issues where the feed does not up date because it can not connect to Twitter… but twitter isn't throwing the failwhale…  Likely you are being hit by the global Twitter API rate_limit.  You can test this if you have command line access on the server that hosts your instance of wordpress by running the following command:

 curl http://twitter.com/account/rate_limit_status.xml

If you see <remaining-hits type="integer">0</remaining-hits> in the returned XML – you are dead – no more UNAUTHENTICATED requests can come from that IP until the hourly rest happend and then only 150 before the IP is locked out again.  It might be nice for a button to be included in the plugin that rund this command and displays the XML for troubleshooting purposes by the end user.

Assuming the above response IS 0 – which is rather likely becuase this plugin is very rock solid – at this point you have a couple of options:

1) Bug the dev team to include the option to have the widgets authenticate as Twitter user for the pull – then you get 150 for that user – and with the default cache of 5 min – a widget will only use 30 of your 150 in an hour – leaving you plenty of "credit" to run your twitter clients all day long.

2) Bug the dev team to make the cache time "configurable" in the widget itself – like a minimum of 5 but up to 60 minutes – that way you should alwyas have "somthing" in the cache.

3) Request the servers IP to be added to a Twitter whitelist for rate limiting – so everyone on the hosted server can play – play – play without fear of being blocked.  This one takes time – not all providers will do it – Twitter won't accept all IP's…  it's just not a super viable solution…

Well – really – all command line access will do is let you easily run that command to prove to yourself that you and others on the server are eating all the allotted API requests from Twitter…  it doesn't "really" fix anything. (you could code a php page really quickly to get that url for you and toss it on your hosted server – it would do the same thing)

Unless you can get the server IP from which these API calls are originating from whitelisted by Twitter…  then you are, mostly, out of options.

Option #2 above is something you can do now – just not through the GUI – You CAN edit the plugin php file and increase the page cache from 300 to 600 or 900 seconds…  Your tweets update less often in the Wordpress widget – but you also use fewer API calls…  In theory (depending on how fast the hosting server is chewing through the API calls) if you set the value to 3600 (cache for 1 hour) – you would show tweets for an hour in the widget, then it would make a request until it could refresh the cache and then hold it for another hour…  the risk is – right at the end of your hour cache the API limit is reached on Twitter and you have to wait until the limit is reset…  same as now.

Really what the plugin needs is the ability to make AUTHENTICATED requests…  but – that's a double edge sword as it will use up some of your 150 personals you get and then leave you without the ability to tweet (well – less tweetability)…  and if you run something like TweetDeck – then you see how fast your allotment can go down…

For you – best approach – ask your hosting provider to open a twitter whitelist request forthe IP's of their server farm…  then cross your fingers.

There you have it – from a terrific developer – the future path…  which will certainly help out a lot of the folks who post here with the "Can not connect" issue.