1. There is no set of "precise launch conditions" that will reliably induce the bug. Sometimes it happens, sometimes it doesn't, without any apparent changes in launch conditions.
2. Even if I gave you my program (almost 30k lines of code) you may never be able to reproduce the bug (even unreliably) because your connection with the servers has different characteristics (latency, speed, warp) from mine here in South Africa.

1. If you put more diagnostic information into that exception thrown by getLastTick (with a view towards exploring why it disagrees with getSubscribedInstruments()), then I can report that diagnostic info to you the next time the bug happens, and this process may lead you to finding the bug.
   
2. We already have information about the bug that could be valuable:
   Let state A be the state in which the API does not exhibit the bug, and state B the state in which the API exhibits the bug.
   • A->B happens unpredictably, but is always accompanied by Java console messages of the form
     "WARNING connect.JForexTaskManager ] Got tick for instrument [EUR/USD] that was not processed by FeedDataProvider..."
     These messages actually seem to contain a lot of diagnostic state information (which was truncated here but can be found in earlier posts).
   • B->A happens by user intervention. The transition can be induced by:
     
     • Opening a new chart of the relevant instrument.
       
     • Subscribing/unsubscribing to any instrument.

Debug.trace("Tester client connecting...");
try{history.getLastTick(Instrument.EURUSD);}catch(JFException ex){Debug.error("Checkpoint C: " + ex);} // diagnostic for bug https://www.dukascopy.com/swiss/english/forex/jforex/forum/viewtopic.php?f=65&t=48927
//connection is needed for data downloading
TesterFactory.getDefaultInstance().connect(
                  "https://www.dukascopy.com/client/demo/jclient/jforex.jnlp",
                  preambleLogin, preamblePassword); // let it throw
try{history.getLastTick(Instrument.EURUSD);}catch(JFException ex){Debug.error("Checkpoint D: " + ex);} // diagnostic for bug https://www.dukascopy.com/swiss/english/forex/jforex/forum/viewtopic.php?f=65&t=48927

package isak.dukamatic.jfs;

import com.dukascopy.api.*;
import com.dukascopy.api.INewsMessage.Action;
import com.dukascopy.api.system.TesterFactory;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.PrintStream;
import java.text.SimpleDateFormat;
import java.util.*;
import java.util.concurrent.atomic.AtomicInteger;

@RequiresFullAccess
public class BugInducingStrategy implements IStrategy {

    @Configurable("Preamble login")
    public String preambleLogin = "DEMO2fDYoE";
    @Configurable("Preamble password")
    public String preamblePassword = "fDYoE";

    private IHistory history;
    private IAccount account;
    private IConsole console;

    private final SimpleDateFormat dateFormat
            = new SimpleDateFormat("yyyy.MM.dd HH:mm:ss.SSS"){{setTimeZone(TimeZone.getTimeZone("GMT"));}};

    public void onTick(Instrument i, ITick t) throws JFException{
        history.getLastTick(Instrument.EURUSD);
    }
    public void onMessage(IMessage im){
        
    }
    public void onAccount(IAccount ia){
        
    }
    public void onStop(){
        
    }
    public void onBar(Instrument i, Period p, IBar b, IBar a){
        
    }

    @Override
    public void onStart(final IContext context) {
            history = context.getHistory();
            account = context.getAccount();
            console = context.getConsole();
            
            console.getOut().println("Checkpoint A: Subscribed to " + context.getSubscribedInstruments() + ".");

            //connection is needed for preamble data downloading
            console.getOut().println("FoundationJfs: Tester client connecting...");
            try {
                try{history.getLastTick(Instrument.EURUSD);}catch(JFException ex){console.getErr().println("Checkpoint B: Subscribed to " + context.getSubscribedInstruments() + ". getLastTick(EURUSD) threw " + ex);} 
// diagnostic for bug https://www.dukascopy.com/swiss/english/forex/jforex/forum/viewtopic.php?f=65&t=48927
                TesterFactory.getDefaultInstance().connect(
                        "https://www.dukascopy.com/client/demo/jclient/jforex.jnlp",
                        preambleLogin, preamblePassword);
                try{history.getLastTick(Instrument.EURUSD);}catch(JFException ex){console.getErr().println("Checkpoint C: Subscribed to " + context.getSubscribedInstruments() + ". getLastTick(EURUSD) threw " + ex);} 
// diagnostic for bug https://www.dukascopy.com/swiss/english/forex/jforex/forum/viewtopic.php?f=65&t=48927
                console.getOut().println("... connect succeeded");
            } catch (Exception ex) {
                context.getConsole().getWarn().println("... connect failed: " + ex);
                //throw new RuntimeException("Failed to connect TesterFactory: " + ex, ex);
            }
    }
}