Why do I get a Boot timeout error (Error R10) when running my app on Heroku?

I have a Java app that I deployed on Heroku. The deployment works like a charm, no errors or warnings and the app starts working. However, after some time, I get the following error:

Error R10 (Boot timeout) -> Web process failed to bind to $PORT within 90 seconds of launch

I do not get any error when I am running my app locally.

FYI: this app periodically checks whether or not there are changes made to a table in a postgresql database and, if so, updates another table in that same database (as far as I can see not really relevant to my problem, but here you go).

Here is the log:

2019-02-12T19:37:15.444651+00:00 heroku[web.1]: Starting process with command `java $JAVA_OPTS -Dserver.port=24637 -cp target/classes:target/dependency/* com.name.numbersbackend.Main`
2019-02-12T19:37:18.657701+00:00 app[web.1]: Setting JAVA_TOOL_OPTIONS defaults based on dyno size. Custom settings will override them.
2019-02-12T19:37:18.660650+00:00 app[web.1]: Picked up JAVA_TOOL_OPTIONS: -Xmx300m -Xss512k -XX:CICompilerCount=2 -Dfile.encoding=UTF-8 
2019-02-12T19:37:35.580329+00:00 app[web.1]: .
2019-02-12T19:37:51.105807+00:00 app[web.1]: .
2019-02-12T19:38:06.683974+00:00 app[web.1]: .
2019-02-12T19:38:22.198062+00:00 app[web.1]: .
2019-02-12T19:38:37.792613+00:00 app[web.1]: .
2019-02-12T19:38:45.489753+00:00 heroku[web.1]: Error R10 (Boot timeout) -> Web process failed to bind to $PORT within 90 seconds of launch
2019-02-12T19:38:45.489753+00:00 heroku[web.1]: Stopping process with SIGKILL
2019-02-12T19:38:45.663859+00:00 heroku[web.1]: Process exited with status 137
2019-02-12T19:38:45.682773+00:00 heroku[web.1]: State changed from starting to crashed
2019-02-12T19:38:45.766843+00:00 heroku[web.1]: State changed from crashed to starting
2019-02-12T19:38:48.871480+00:00 heroku[web.1]: Starting process with command `java $JAVA_OPTS -Dserver.port=39010 -cp target/classes:target/dependency/* com.name.numbersbackend.Main`
2019-02-12T19:38:51.074950+00:00 app[web.1]: Setting JAVA_TOOL_OPTIONS defaults based on dyno size. Custom settings will override them.
2019-02-12T19:38:51.077995+00:00 app[web.1]: Picked up JAVA_TOOL_OPTIONS: -Xmx300m -Xss512k -XX:CICompilerCount=2 -Dfile.encoding=UTF-8 
2019-02-12T19:39:07.724633+00:00 app[web.1]: .
2019-02-12T19:39:23.250203+00:00 app[web.1]: .
2019-02-12T19:39:38.760492+00:00 app[web.1]: .
2019-02-12T19:39:54.313859+00:00 app[web.1]: .
2019-02-12T19:40:09.881207+00:00 app[web.1]: .
2019-02-12T19:40:19.374407+00:00 heroku[web.1]: State changed from starting to crashed
2019-02-12T19:40:19.187236+00:00 heroku[web.1]: Error R10 (Boot timeout) -> Web process failed to bind to $PORT within 90 seconds of launch
2019-02-12T19:40:19.187351+00:00 heroku[web.1]: Stopping process with SIGKILL
2019-02-12T19:40:19.354497+00:00 heroku[web.1]: Process exited with status 137

FYI: The line 2019-02-12T19:39:38.760492+00:00 app[web.1]: . (and lines like this) contains some temporary output from my app to show that it is actually doing something. For each of these lines, the program is checking if there are changes to the table and if so, if it needs to take action (if it does need to take action, the output of the app is more meaningful).

As you can see, the app is starting alright, working for some time, then crashes and even restarts. However, at some point it stops working entirely.

Here is my pom.xml:

<?xml version="1.0" encoding="UTF-8"?>
<project xmlns="http://maven.apache.org/POM/4.0.0"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
    <modelVersion>4.0.0</modelVersion>

    <groupId>com.name</groupId>
    <artifactId>com.name.app.backend</artifactId>
    <version>1.0</version>
    <build>
        <plugins>
            <plugin>
                <groupId>org.apache.maven.plugins</groupId>
                <artifactId>maven-dependency-plugin</artifactId>
                <version>3.0.1</version>
                <executions>
                    <execution>
                        <id>copy-dependencies</id>
                        <phase>package</phase>
                        <goals>
                            <goal>copy-dependencies</goal>
                        </goals>
                    </execution>
                </executions>
            </plugin>
            <plugin>
                <groupId>org.apache.maven.plugins</groupId>
                <artifactId>maven-compiler-plugin</artifactId>
                <version>2.3.2</version>
                <configuration>
                    <source>8</source>
                    <target>8</target>
                </configuration>
            </plugin>
        </plugins>
    </build>
    <repositories>
        <repository>
            <id>jitpack.io</id>
            <url>https://jitpack.io</url>
        </repository>
    </repositories>
    <properties>
        <project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
    </properties>
    <dependencies>
        <!-- https://mvnrepository.com/artifact/org.json/json -->
        <dependency>
            <groupId>org.json</groupId>
            <artifactId>json</artifactId>
            <version>20180813</version>
        </dependency>
        <!-- https://mvnrepository.com/artifact/org.postgresql/postgresql -->
        <dependency>
            <groupId>org.postgresql</groupId>
            <artifactId>postgresql</artifactId>
            <version>42.2.5</version>
        </dependency>
        <dependency>
            <groupId>com.github.myname</groupId>
            <artifactId>app-lib</artifactId>
            <version>master-SNAPSHOT</version>
        </dependency>
    </dependencies>
</project>

...and my Procfile:

web: java $JAVA_OPTS -Dserver.port=$PORT -cp target/classes:target/dependency/* nl.limakajo.numbersbackend.Main

After a lot of Googling and browsing on SO, I have not found a solution.