Update: November 18 2017
AllMyShares relies on Yahoo! Finance API's for (20 minute delayed) stock quotes and historical stock prices (end of day) data.
However, these APIs have been discontinued by Yahoo! and Yahoo! will not be reintroducing that functionality. The reason (stated by Yahoo!) for the withdrawal of the Yahoo! Finance API is that the terms of service for the API were being violated (https://developer.yahoo.com/terms/).
As an alternative, some comprehensive and high quality stock data APIs do exist, but they cater to banks and financial institutions and cost tens of thousands of dollars per year. AllMyShares was designed to operate in several countries with several stock markets. The high quality API's mentioned are charged per stock market. Several options have been considered - each would require significant change to the AllMyShares business model. It is simply not possible to provide this data without a subscription business model. As per the cost of this subscription per user - it is unknown.
Yahoo! Finance withdrew their historical stock price API. This meant that AllMyShares timelines no longer worked. The remainder of the AllMyShares app continued to work, however AllMyShares was immediately withdrawn from sale on the Apple App Store.
21 March '17
The AllMyShares app was removed from sale on the Apple App Store. It was decided that the app would be withdrawn rather than offering reduced functionality.
Dropbox changed their API (for exporting data from the app to a computer). AllMyShares developers created a fix with the intent of reinstating a version of AllMyShares (without historical analysis)... and providing a Dropbox update to existing users. However, events of October '17 (see below) made this not viable.'
Yahoo! Finance withdrew their API for (20 minute delayed) stock quotes. This meant that the AllMyShares app could no longer retrieve any (20 minute delayed) quotes for stocks.
AllMyShares is researching alternative sources of data and alternative business models, but the app remains (indefinitely) unavailable on the app store. AllMyShares was released in 2008 and apologises to all users of the app.